Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter. More...

Detailed Description

Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter.

See the documentation of pm_fftnr for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of size getExpNext(size(data), 2) of the same type and kind as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftnr, only: getFFTI

type_of(data) :: fft(1 : getExpNext(size(data)))

fft(:) = getFFTI(data(:))

pm_fftnr::getFFTI
Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequen...
Definition: pm_fftnr.F90:428

pm_fftnr
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftnr.F90:184

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTR.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftnr, only: getFFTF, getFFTI

6 use pm_distUnif, only: getUnifRand

7 use pm_mathCompare, only: isClose

8 use pm_err, only: setAsserted

9

10 implicit none

11

12 integer(IK) :: i

13 integer(IK) :: lenData

14 type(display_type) :: disp

15 disp = display_type(file = "main.out.F90")

16

17 do i = 1, 5

18 block

19 use pm_kind, only: TKC => CK32

20 real(TKC) :: reltol

21 complex(TKC), allocatable :: data(:), atad(:)

22 call disp%show("lenData = getUnifRand(5, 100)")

23 lenData = getUnifRand(5, 100)

24 call disp%show("lenData")

25 call disp%show( lenData )

26 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

27 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

28 call disp%show("data")

29 call disp%show( data )

30 call disp%skip()

31 call disp%show("atad = getFFTI(getFFTF(data))")

32 atad = getFFTI(getFFTF(data))

33 call disp%show("atad")

34 call disp%show( atad )

35 call disp%show("reltol = sqrt(epsilon(1._TKC))")

36 reltol = sqrt(epsilon(1._TKC))

37 call disp%show("reltol")

38 call disp%show( reltol )

39 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

40 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

41 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

42 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

43 call disp%skip()

44 end block

45

46 block

47 use pm_kind, only: TKC => CK64

48 real(TKC) :: reltol

49 complex(TKC), allocatable :: data(:), atad(:)

50 call disp%show("lenData = getUnifRand(5, 100)")

51 lenData = getUnifRand(5, 100)

52 call disp%show("lenData")

53 call disp%show( lenData )

54 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

55 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

56 call disp%show("data")

57 call disp%show( data )

58 call disp%skip()

59 call disp%show("atad = getFFTI(getFFTF(data))")

60 atad = getFFTI(getFFTF(data))

61 call disp%show("atad")

62 call disp%show( atad )

63 call disp%show("reltol = sqrt(epsilon(1._TKC))")

64 reltol = sqrt(epsilon(1._TKC))

65 call disp%show("reltol")

66 call disp%show( reltol )

67 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

68 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

69 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

70 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

71 call disp%skip()

72 end block

73

74 block

75 use pm_kind, only: TKC => CKH

76 real(TKC) :: reltol

77 complex(TKC), allocatable :: data(:), atad(:)

78 call disp%show("lenData = getUnifRand(5, 100)")

79 lenData = getUnifRand(5, 100)

80 call disp%show("lenData")

81 call disp%show( lenData )

82 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

83 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

84 call disp%show("data")

85 call disp%show( data )

86 call disp%skip()

87 call disp%show("atad = getFFTI(getFFTF(data))")

88 atad = getFFTI(getFFTF(data))

89 call disp%show("atad")

90 call disp%show( atad )

91 call disp%show("reltol = sqrt(epsilon(1._TKC))")

92 reltol = sqrt(epsilon(1._TKC))

93 call disp%show("reltol")

94 call disp%show( reltol )

95 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

96 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

97 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

98 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

99 call disp%skip()

100 end block

101

102 block

103 use pm_kind, only: TKC => RK32

104 real(TKC) :: reltol

105 real(TKC), allocatable :: data(:), atad(:)

106 call disp%show("lenData = getUnifRand(5, 100)")

107 lenData = getUnifRand(5, 100)

108 call disp%show("lenData")

109 call disp%show( lenData )

110 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

111 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

112 call disp%show("data")

113 call disp%show( data )

114 call disp%skip()

115 call disp%show("atad = getFFTI(getFFTF(data))")

116 atad = getFFTI(getFFTF(data))

117 call disp%show("atad")

118 call disp%show( atad )

119 call disp%show("reltol = sqrt(epsilon(1._TKC))")

120 reltol = sqrt(epsilon(1._TKC))

121 call disp%show("reltol")

122 call disp%show( reltol )

123 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

124 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

125 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

126 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

127 call disp%skip()

128 end block

129

130 block

131 use pm_kind, only: TKC => RK64

132 real(TKC) :: reltol

133 real(TKC), allocatable :: data(:), atad(:)

134 call disp%show("lenData = getUnifRand(5, 100)")

135 lenData = getUnifRand(5, 100)

136 call disp%show("lenData")

137 call disp%show( lenData )

138 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

139 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

140 call disp%show("data")

141 call disp%show( data )

142 call disp%skip()

143 call disp%show("atad = getFFTI(getFFTF(data))")

144 atad = getFFTI(getFFTF(data))

145 call disp%show("atad")

146 call disp%show( atad )

147 call disp%show("reltol = sqrt(epsilon(1._TKC))")

148 reltol = sqrt(epsilon(1._TKC))

149 call disp%show("reltol")

150 call disp%show( reltol )

151 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

152 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

153 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

154 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

155 call disp%skip()

156 end block

157

158 block

159 use pm_kind, only: TKC => RKH

160 real(TKC) :: reltol

161 real(TKC), allocatable :: data(:), atad(:)

162 call disp%show("lenData = getUnifRand(5, 100)")

163 lenData = getUnifRand(5, 100)

164 call disp%show("lenData")

165 call disp%show( lenData )

166 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

167 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

168 call disp%show("data")

169 call disp%show( data )

170 call disp%skip()

171 call disp%show("atad = getFFTI(getFFTF(data))")

172 atad = getFFTI(getFFTF(data))

173 call disp%show("atad")

174 call disp%show( atad )

175 call disp%show("reltol = sqrt(epsilon(1._TKC))")

176 reltol = sqrt(epsilon(1._TKC))

177 call disp%show("reltol")

178 call disp%show( reltol )

179 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

180 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

181 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

182 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

183 call disp%skip()

184 end block

185 end do

186

187end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4106

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1617

pm_fftnr::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11074

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:523

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:10962

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:28

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:281

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:477

pm_kind::RK32
integer, parameter RK32
The real kind for a 32-bits container.
Definition: pm_kind.F90:294

pm_kind::CK64
integer, parameter CK64
The complex kind for a 64-bits container.
Definition: pm_kind.F90:290

pm_kind::CK32
integer, parameter CK32
The complex kind for a 32-bits container.
Definition: pm_kind.F90:291

pm_kind::RK64
integer, parameter RK64
The real kind for a 64-bits container.
Definition: pm_kind.F90:293

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:280

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:279

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind a...
Definition: pm_kind.F90:462

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10228

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_intel* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte_fortran_*_intel*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_gnu* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+85

4data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

5data

6(+1.72630918, +0.255782068), (+1.82257116, +0.360711992), (+1.90233564, +0.787378728), (+1.93223429, +0.258641303), (+1.08092785, +0.487582505), (+1.34929490, +0.682230175), (+1.01557374, +0.879168510), (+1.22697687, +0.260682642), (+1.15125203, +0.820527196), (+1.32199645, +0.998360276), (+1.03833425, +0.505837858), (+1.28495693, +0.529098272), (+1.59083557, +0.427102983), (+1.35849154, +0.103182018), (+1.35760856, +0.282749355), (+1.64291060, +0.562081575), (+1.22520161, +0.184685886), (+1.18583989, +0.941054583), (+1.26293933, +0.198905349), (+1.52017891, +0.624573827), (+1.46348262, +0.786550105), (+1.82653129, +0.606297553), (+1.20034432, +0.412724972), (+1.96202970, +0.136664331), (+1.92350912, +0.510044992), (+1.96301270, +0.753729224), (+1.59709048, +0.451031208), (+1.14431322, +0.431270182), (+1.04715800, +0.742725313), (+1.57712960, +0.159049690), (+1.87320209, +0.246391118), (+1.92080855, +0.502821684), (+1.65424681, +0.224322081E-1), (+1.81740618, +0.888709486), (+1.03956342, +0.781625569), (+1.17658305, +0.610794961), (+1.91552424, +0.692885101), (+1.69637036, +0.990594923), (+1.31864476, +0.687885940), (+1.18173432, +0.913963258), (+1.60445988, +0.270027280), (+1.16150987, +0.603002846), (+1.37685359, +0.953729808), (+1.11025453, +0.476669014), (+1.20573640, +0.465976954), (+1.47212982, +0.184807360), (+1.00405741, +0.631133020), (+1.38557422, +0.226339281), (+1.16202760, +0.702522218), (+1.76558542, +0.373244166), (+1.20772290, +0.769840419), (+1.62920833, +0.850589871E-1), (+1.91407347, +0.917089701), (+1.88492250, +0.873724580), (+1.91990674, +0.638290048E-1), (+1.15241694, +0.913243949), (+1.35287666, +0.549920440), (+1.22910321, +0.369035482), (+1.89220405, +0.360608101), (+1.18047106, +0.477833331), (+1.62609863, +0.643243015), (+1.41912913, +0.910847187), (+1.04554760, +0.198077857), (+1.48037314, +0.755422354), (+1.32635403, +0.991707087), (+1.74117494, +0.140441895), (+1.27051616, +0.753087044), (+1.08385777, +0.347631752), (+1.29644430, +0.905484200), (+1.45970941, +0.442749143), (+1.83417821, +0.542314827), (+1.52601159, +0.288592875), (+1.31324565, +0.463233829), (+1.24187016, +0.204844832), (+1.28054309, +0.819141805), (+1.64311314, +0.294269383), (+1.87613845, +0.699461520), (+1.02093768, +0.558885813), (+1.19249582, +0.906204343), (+1.16256380, +0.751355708), (+1.51537561, +0.976802349), (+1.28489518, +0.292988181), (+1.86794281, +0.245032191), (+1.64675999, +0.133970559), (+1.22664261, +0.392673135)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.72630930, +0.255782068), (+1.82257104, +0.360712171), (+1.90233517, +0.787378669), (+1.93223393, +0.258641362), (+1.08092773, +0.487582386), (+1.34929478, +0.682230055), (+1.01557374, +0.879168510), (+1.22697663, +0.260682493), (+1.15125191, +0.820527136), (+1.32199645, +0.998360395), (+1.03833425, +0.505837798), (+1.28495681, +0.529098392), (+1.59083557, +0.427103072), (+1.35849166, +0.103182107), (+1.35760868, +0.282749474), (+1.64291048, +0.562081575), (+1.22520161, +0.184686005), (+1.18583989, +0.941054702), (+1.26293921, +0.198905572), (+1.52017891, +0.624573767), (+1.46348250, +0.786550164), (+1.82653117, +0.606297553), (+1.20034409, +0.412725002), (+1.96202922, +0.136664450), (+1.92350912, +0.510045171), (+1.96301246, +0.753729463), (+1.59709048, +0.451031268), (+1.14431310, +0.431270242), (+1.04715800, +0.742725372), (+1.57712960, +0.159049973), (+1.87320185, +0.246391132), (+1.92080832, +0.502821624), (+1.65424705, +0.224321131E-1), (+1.81740618, +0.888709366), (+1.03956318, +0.781625271), (+1.17658305, +0.610794544), (+1.91552424, +0.692884803), (+1.69637048, +0.990594625), (+1.31864488, +0.687885821), (+1.18173432, +0.913962960), (+1.60445988, +0.270027310), (+1.16150975, +0.603002787), (+1.37685347, +0.953729570), (+1.11025429, +0.476668954), (+1.20573640, +0.465976894), (+1.47212970, +0.184807375), (+1.00405729, +0.631133020), (+1.38557410, +0.226339191), (+1.16202784, +0.702522159), (+1.76558542, +0.373244166), (+1.20772266, +0.769840360), (+1.62920821, +0.850588232E-1), (+1.91407335, +0.917089462), (+1.88492250, +0.873724282), (+1.91990662, +0.638288558E-1), (+1.15241671, +0.913243413), (+1.35287666, +0.549920380), (+1.22910309, +0.369035482), (+1.89220369, +0.360607982), (+1.18047082, +0.477833211), (+1.62609851, +0.643242955), (+1.41912889, +0.910847068), (+1.04554772, +0.198077649), (+1.48037291, +0.755422294), (+1.32635427, +0.991707146), (+1.74117494, +0.140441880), (+1.27051592, +0.753086925), (+1.08385766, +0.347631812), (+1.29644430, +0.905484259), (+1.45970953, +0.442749113), (+1.83417821, +0.542314529), (+1.52601123, +0.288592786), (+1.31324542, +0.463233888), (+1.24187016, +0.204844952), (+1.28054273, +0.819141865), (+1.64311278, +0.294269413), (+1.87613821, +0.699461699), (+1.02093768, +0.558885932), (+1.19249594, +0.906204522), (+1.16256380, +0.751355767), (+1.51537561, +0.976802409), (+1.28489518, +0.292988062), (+1.86794257, +0.245032087), (+1.64675987, +0.133970425), (+1.22664249, +0.392673135), (+0.298023224E-6, +0.596046448E-7), (+0.417232513E-6, +0.298023224E-7), (+0.417232513E-6, +0.596046448E-7), (+0.596046448E-7, -0.894069672E-7), (+0.119209290E-6, -0.894069672E-7), (+0.596046448E-7, +0.745058060E-7), (+0.178813934E-6, -0.193715096E-6), (-0.596046448E-7, -0.149011612E-6), (-0.119209290E-6, -0.253319740E-6), (+0.596046448E-7, +0.596046448E-7), (+0.178813934E-6, -0.596046448E-7), (+0.596046448E-7, +0.214204192E-6), (+0.596046448E-7, +0.178813934E-6), (-0.178813934E-6, +0.149011612E-6), (+0.596046448E-7, +0.149011612E-6), (-0.596046448E-7, +0.327825546E-6), (+0.119209290E-6, +0.149011612E-6), (+0.119209290E-6, +0.417232513E-6), (+0.178813934E-6, +0.268220901E-6), (+0.00000000, +0.298023224E-7), (+0.298023224E-6, +0.00000000), (+0.00000000, +0.178813934E-6), (+0.596046448E-7, -0.596046448E-7), (+0.596046448E-7, +0.134110451E-6), (+0.00000000, -0.447034836E-7), (+0.119209290E-6, +0.178813934E-6), (+0.238418579E-6, +0.298023224E-7), (+0.357627869E-6, -0.298023224E-7), (+0.178813934E-6, +0.163912773E-6), (+0.00000000, +0.238418579E-6), (+0.357627869E-6, +0.193715096E-6), (+0.00000000, +0.238418579E-6), (+0.178813934E-6, +0.178813934E-6), (+0.298023224E-6, +0.387430191E-6), (+0.298023224E-6, +0.208616257E-6), (+0.238418579E-6, -0.596046448E-7), (+0.357627869E-6, -0.298023224E-7), (+0.119209290E-6, +0.119209290E-6), (+0.238418579E-6, +0.163912773E-6), (+0.00000000, +0.298023224E-7), (+0.178813934E-6, -0.298023224E-7), (+0.119209290E-6, +0.193715096E-6), (+0.178813934E-6, +0.178813934E-6)

11reltol = sqrt(epsilon(1._TKC))

12reltol

13+0.345266977E-3

14isClose(data, atad(1:size(data)), reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+51

21data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

22data

23(+1.4635145603256441, +0.83902294597368787), (+1.5416501730344918, +0.38391896195024589E-1), (+1.0888497999645135, +0.25264527384370150), (+1.2391000510310379, +0.16109616736866739), (+1.3997169097341560, +0.81538278759023075), (+1.3911622878235128, +0.29145747307665759), (+1.3644958478058622, +0.95269617051452848), (+1.2556007342170621, +0.62957141809552430), (+1.5803264472710805, +0.14904721338722360), (+1.7698444035818168, +0.15341042989335740), (+1.1580198241072284, +0.22800210876238391), (+1.1630756186013413, +0.64378510769404240), (+1.3418705153837656, +0.53949892406634170), (+1.9261705154352078, +0.58592234051311454), (+1.9924064232631089, +0.85622128142494036E-1), (+1.4250219226654623, +0.80453836557401548), (+1.1285149390726414, +0.37594628808583219), (+1.8648932950795607, +0.26787776643713312), (+1.2397202995661165, +0.14270818352449532), (+1.4537593924918546, +0.20094353312144952), (+1.9405231796534457, +0.92823076957259543), (+1.7274790975298266, +0.43975859870447032), (+1.3602226979192444, +0.60986693022234562), (+1.9871954399688718, +0.53824626688493105), (+1.8122618026622090, +0.97418273115906540), (+1.8857624076037780, +0.65628665512232343), (+1.1750129421988436, +0.56572250579195316), (+1.4230115338687142, +0.23959896133819747), (+1.7488481138329071, +0.71439718200503111), (+1.2728759200938735, +0.17477221017372124), (+1.2596191759156947, +0.80314340010638241), (+1.4642802923060469, +0.28714625314858144), (+1.3594722713230314, +0.32597679520415235), (+1.4538423069088946, +0.39591171406774961), (+1.6012603894773016, +0.24298115933223308), (+1.7440330437075593, +0.56605843885554619), (+1.9240334124176521, +0.81794423426002394), (+1.1707689634965466, +0.83241326348521338), (+1.1084363116738427, +0.19312535112599749), (+1.9907275119487375, +0.68044205299277660), (+1.6702415553297856, +0.33488225915890402E-1), (+1.5390714321175571, +0.44784542418612727), (+1.3214105906140388, +0.94517238156594596), (+1.9153560390124644, +0.57715400690777774), (+1.6506023296157992, +0.60931014057807875), (+1.3316210296810091, +0.54778713048720173), (+1.5144852940273719, +0.98595951669941762), (+1.9453499070933513, +0.13498102248388288), (+1.8264483946969881, +0.70653143349495107), (+1.7624039981197095, +0.22570673367896199), (+1.1962848729985889, +0.24131363013728280)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.4635145603256443, +0.83902294597368798), (+1.5416501730344918, +0.38391896195024783E-1), (+1.0888497999645128, +0.25264527384370195), (+1.2391000510310377, +0.16109616736866766), (+1.3997169097341560, +0.81538278759023086), (+1.3911622878235133, +0.29145747307665770), (+1.3644958478058622, +0.95269617051452848), (+1.2556007342170616, +0.62957141809552430), (+1.5803264472710803, +0.14904721338722396), (+1.7698444035818168, +0.15341042989335760), (+1.1580198241072279, +0.22800210876238458), (+1.1630756186013409, +0.64378510769404262), (+1.3418705153837656, +0.53949892406634192), (+1.9261705154352082, +0.58592234051311465), (+1.9924064232631085, +0.85622128142494258E-1), (+1.4250219226654619, +0.80453836557401570), (+1.1285149390726414, +0.37594628808583214), (+1.8648932950795609, +0.26787776643713307), (+1.2397202995661163, +0.14270818352449532), (+1.4537593924918544, +0.20094353312144972), (+1.9405231796534459, +0.92823076957259520), (+1.7274790975298271, +0.43975859870447048), (+1.3602226979192444, +0.60986693022234539), (+1.9871954399688718, +0.53824626688493127), (+1.8122618026622090, +0.97418273115906506), (+1.8857624076037782, +0.65628665512232354), (+1.1750129421988436, +0.56572250579195316), (+1.4230115338687144, +0.23959896133819750), (+1.7488481138329071, +0.71439718200503100), (+1.2728759200938740, +0.17477221017372127), (+1.2596191759156947, +0.80314340010638219), (+1.4642802923060467, +0.28714625314858139), (+1.3594722713230316, +0.32597679520415240), (+1.4538423069088946, +0.39591171406774983), (+1.6012603894773012, +0.24298115933223308), (+1.7440330437075588, +0.56605843885554608), (+1.9240334124176519, +0.81794423426002405), (+1.1707689634965466, +0.83241326348521349), (+1.1084363116738425, +0.19312535112599744), (+1.9907275119487373, +0.68044205299277660), (+1.6702415553297854, +0.33488225915890422E-1), (+1.5390714321175567, +0.44784542418612727), (+1.3214105906140381, +0.94517238156594574), (+1.9153560390124640, +0.57715400690777741), (+1.6506023296157992, +0.60931014057807875), (+1.3316210296810089, +0.54778713048720151), (+1.5144852940273714, +0.98595951669941728), (+1.9453499070933509, +0.13498102248388272), (+1.8264483946969881, +0.70653143349495084), (+1.7624039981197093, +0.22570673367896191), (+1.1962848729985891, +0.24131363013728280), (+0.0000000000000000, -0.24980018054066022E-15), (-0.22204460492503131E-15, +0.22204460492503131E-15), (-0.11102230246251565E-15, -0.38857805861880479E-15), (+0.11102230246251565E-15, +0.27755575615628914E-15), (-0.22204460492503131E-15, -0.16653345369377348E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (-0.22204460492503131E-15, +0.0000000000000000), (+0.33306690738754696E-15, +0.33306690738754696E-15), (+0.44408920985006262E-15, +0.83266726846886741E-16), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.33306690738754696E-15, -0.83266726846886741E-16), (+0.33306690738754696E-15, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15)

28reltol = sqrt(epsilon(1._TKC))

29reltol

30+0.14901161193847656E-7

31isClose(data, atad(1:size(data)), reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+93

38data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

39data

40(+1.24978699847097007004119710421378653, +0.684789310951315168593932266455355089), (+1.94037079403756905834159660049347490, +0.264544787060060006077381073035274520), (+1.99397346836646298143511354167458993, +0.361113788578946723930000923237627548), (+1.57257972922091490865297869657154584, +0.839384978163805237577076330468163919), (+1.65015212842946397588662091437795568, +0.689504041773494058900583183375248954), (+1.44272189333285761327533528894839149, +0.393777425310520356399442958999154403), (+1.17482019594676351799345395008824238, +0.504183879532479359741357686177824578E-1), (+1.00092219003825519671711140997560086, +0.969361905193840887269321225445166993), (+1.59238154998577585112890134066716601, +0.690200038076518065596852198068619040), (+1.26708259436024532417517369257296069, +0.355804293851916490741995520495427634), (+1.67762498543033816174747281286715625, +0.382009942825241571179749541477629531), (+1.24322198829926834303768913026550097, +0.969901736725870283568508811862428841), (+1.99462292690791044143394270805056196, +0.252874973829236446235709229263261593), (+1.51945091292423570830515164023007274, +0.848833582533833083250426392906531323E-1), (+1.43345538008436407046991658830579560, +0.991232152501436555988952357944316119), (+1.11949738694506411357197803361284788, +0.899917258287199491627935588811700220), (+1.62883214205201124013204206374098066, +0.991433359191962212398092794603511566), (+1.93121416674148019194012965195856644, +0.269039609433180828980569369811182353), (+1.16426366405348218218599338749129162, +0.592772533169530436494304437785241906E-1), (+1.40934014178875211552049698979926255, +0.446286511621266335857285018502135765), (+1.87764337224639262376847164514084883, +0.540780957687926460441032452202666941), (+1.91396472088922996990587953192131662, +0.671557080986893577451022968609383742), (+1.04659137170288177075631142987980799, +0.662948883406190325058319783336844025), (+1.45270621201855552703458954125565588, +0.898083833439845038916795997736432371), (+1.71976893365909552511233481680066655, +0.575453454010804236334952360945795145E-1), (+1.79638200271093758818075181830524196, +0.903904064093843303828455394002187775), (+1.69914502008538954178742449786800950, +0.937815535946448951934010292084181737E-1), (+1.85583246268964179321984048810627874, +0.870594776734222796037472359814839313), (+1.23070056108752859880238691189340263, +0.448890381492270550879111140371451606), (+1.53786870453380168356640079859222700, +0.828718698404752161423595077994850789), (+1.42344137176289866707940676960799483, +0.847818679725421542823384343077692934), (+1.08645324952169356274578450711250328, +0.547101980024401845724410411966728920), (+1.83031644569088185389015530700126423, +0.795781161416790657070917959680491632E-2), (+1.93396124594160593337385855569441518, +0.847012654221215621821281437790685478E-1), (+1.10992188451752965943289390030850173, +0.280591436473296284932124474993504366), (+1.87482267692934006033559053316768283, +0.517256649823276954951512403416124888), (+1.81676961218091723534523387660660730, +0.705378287821628707961391784248571221), (+1.02523899822511334744514175078293469, +0.375747711971450422832183825146300642), (+1.72330965007406780400422793120718383, +0.940266942511309285299001717447013799), (+1.66309957580578396281435447448334019, +0.234701149730822383931909893799956617), (+1.65469878739027884102041055397129005, +0.286782333770249255229805153279499396), (+1.43747685794651461993315045595213948, +0.296189340579595143125389720448500070), (+1.33647615717233300828058476782669901, +0.664318248687530946059498995715186568), (+1.79304627666432883531828239908531734, +0.673124814428050186376610791497623362), (+1.18200436214559141792523701732221751, +0.946276349231947002074137215429207191E-1), (+1.41003675110842266548285910326658843, +0.622163957409090342882326277166418838), (+1.48238740050420899502587186628812431, +0.231362029722185931361180219397219562E-1), (+1.09940686620461939678616234065953672, +0.590350303925600581728227867421662760), (+1.33108150431279309576737461972289144, +0.814533105557954627020708912960864196), (+1.57996617561773854279471949883319265, +0.188191079668341147797200578136566391), (+1.81595002276865470662209054048993655, +0.309128648846619795774927977288159799), (+1.40973374105662135928933587220110129, +0.694729214395833463994608833278300250E-1), (+1.66762360102802618971701684123465579, +0.629750607554979317305632393587473691), (+1.93091713391275807826911907686156010, +0.932960780159104316603889956185501809), (+1.20475982556624674626473464905346116, +0.420097871147860470259964202540710442), (+1.60451105022705921759377636307741839, +0.143094193644884034548845106222195039), (+1.82008401649175430398775553047016990, +0.866512104137205386180439565153359537), (+1.79056804882840366805876726620050686, +0.910412773953368660602564218956630085), (+1.34447861985801352699166403571615383, +0.729393749779389567265181151908083535), (+1.22424657294781823839746380171306701, +0.731284943937557032501816180688474812), (+1.39938421594631681607050444501863623, +0.143373837656150300264863353875908274), (+1.08441703932123745617369636759658533, +0.185019531164770865991338100297108471), (+1.01820316670435801718861974338408404, +0.277506131324718492581590152165731581), (+1.11879775691755067264095868080814644, +0.255840036103159103393964301313497932), (+1.16261409446641005694071997340352749, +0.571856001327907150137440961160397599), (+1.94716965070126085366375715309995634, +0.379886319901143783007014869782128538), (+1.32754559676873844419262001916320232, +0.729520575658831596648294393835418583), (+1.91444749050971880717791047498856399, +0.535390037665488176517732637026007718), (+1.82228513514399423958376726795750678, +0.226352738959670913977938250095427173), (+1.52905439453772269240068300746279149, +0.213280823578679135507033788643480785), (+1.52746930765716301578877600555333983, +0.889573192106029203619625798677694893), (+1.37464071047563081320609137412427550, +0.862826690763336380332348379403597922), (+1.11844990322140523319683124233066044, +0.406420166292809354010763204484404573), (+1.51413156525704091620973508319051010, +0.550014040168049284594665361315325936), (+1.19007265385390353614939990241090188, +0.501441734927672466358617704849920592), (+1.71726285991730484829790030537677590, +0.332684227638619420366541789596323896), (+1.69995348190901380153889241902944693, +0.950516338592782374388312551470062621), (+1.44129290539746738794027480551318576, +0.740521425682155442250439994586866630), (+1.50470100598421693082742001233429980, +0.772115637816338141802204921961859075), (+1.38372265411224507347136144472352922, +0.655524149352090818548892470614229716), (+1.12984038285458267572350268122920561, +0.878757254839839022020513285703764662), (+1.14832967380346428382764253114396895, +0.386696030897589012695039077321056759), (+1.09119607060216751356030496324278262, +0.117211154785431424418681438069983318), (+1.56611901073370817388538947052307642, +0.130346134893613605622862959434624887), (+1.27039450642809681697659260132506465, +0.346689375676707573560436407213486325), (+1.83385573936621743247237161670687837, +0.904671272388742738156959800093572286), (+1.39371419933932161507147027213701872, +0.143807305976543526478259967093359999), (+1.12990930796802894304944986297054172, +0.143549898383322836097224417784872756), (+1.12254369764768974033426281843405660, +0.361239564684732685479225608672218585), (+1.05942750971702419649407145090467262, +0.645735478124142751407921499255398766), (+1.95238033561017329840013105357935251, +0.134193780939824147434491843704652941), (+1.11202878413172985925555314653376728, +0.967307326033015995719652677976556654), (+1.42251426142101082415389455700262799, +0.590918515918112131119173011537356877)

41

42atad = getFFTI(getFFTF(data))

43atad

44(+1.24978699847097007004119710421378633, +0.684789310951315168593932266455354993), (+1.94037079403756905834159660049347528, +0.264544787060060006077381073035274279), (+1.99397346836646298143511354167458993, +0.361113788578946723930000923237627692), (+1.57257972922091490865297869657154584, +0.839384978163805237577076330468163919), (+1.65015212842946397588662091437795529, +0.689504041773494058900583183375248954), (+1.44272189333285761327533528894839149, +0.393777425310520356399442958999154114), (+1.17482019594676351799345395008824238, +0.504183879532479359741357686177821207E-1), (+1.00092219003825519671711140997560047, +0.969361905193840887269321225445166704), (+1.59238154998577585112890134066716601, +0.690200038076518065596852198068618944), (+1.26708259436024532417517369257296069, +0.355804293851916490741995520495427537), (+1.67762498543033816174747281286715682, +0.382009942825241571179749541477629531), (+1.24322198829926834303768913026550078, +0.969901736725870283568508811862429130), 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(+1.09119607060216751356030496324278281, +0.117211154785431424418681438069983246), (+1.56611901073370817388538947052307680, +0.130346134893613605622862959434624887), (+1.27039450642809681697659260132506465, +0.346689375676707573560436407213485988), (+1.83385573936621743247237161670687914, +0.904671272388742738156959800093572479), (+1.39371419933932161507147027213701930, +0.143807305976543526478259967093359854), (+1.12990930796802894304944986297054172, +0.143549898383322836097224417784872659), (+1.12254369764768974033426281843405641, +0.361239564684732685479225608672218488), (+1.05942750971702419649407145090467262, +0.645735478124142751407921499255398766), (+1.95238033561017329840013105357935270, +0.134193780939824147434491843704652941), (+1.11202878413172985925555314653376709, +0.967307326033015995719652677976556943), (+1.42251426142101082415389455700262837, +0.590918515918112131119173011537356877), (-0.192592994438723585305597794258492732E-33, 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-0.409260113182287618774395312799297055E-33), (-0.577778983316170755916793382775478196E-33, -0.216667118743564033468797518540804323E-33), (-0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33), (-0.674075480535532548569592279904724561E-33, -0.433334237487128066937595037081608647E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.674075480535532548569592279904724561E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, -0.264815367353244929795196967105427506E-33), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.144444745829042688979198345693869549E-33), (-0.481482486096808963263994485646231830E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-33), (-0.385185988877447170611195588516985464E-33, -0.433334237487128066937595037081608647E-33), (+0.962964972193617926527988971292463659E-34, -0.529630734706489859590393934210855013E-33), (-0.481482486096808963263994485646231830E-33, -0.625927231925851652243192831340101379E-33), (+0.962964972193617926527988971292463659E-34, -0.132407683676622464897598483552713753E-33), (-0.481482486096808963263994485646231830E-33, -0.409260113182287618774395312799297055E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.216667118743564033468797518540804323E-33)

45reltol = sqrt(epsilon(1._TKC))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, atad(1:size(data)), reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+47

55data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

56data

57+1.74671495, +1.47724867, +1.58584166, +1.26332402, +1.08800197, +1.05452299, +1.19437456, +1.92438269, +1.42765856, +1.80639529, +1.80188847, +1.66945982, +1.43477559, +1.71067047, +1.76397157, +1.35328698, +1.62448907, +1.31963706, +1.89810133, +1.76322150, +1.15715015, +1.36749315, +1.12635589, +1.08005977, +1.85237932, +1.88313949, +1.25063539, +1.71657228, +1.95433998, +1.83385515, +1.23069537, +1.53223991, +1.18322206, +1.80132627, +1.59068406, +1.69172740, +1.12441063, +1.23369932, +1.67175245, +1.95647001, +1.14383745, +1.56362307, +1.02746153, +1.82899356, +1.53953981, +1.02995992, +1.48216391

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.74671531, +1.47724879, +1.58584142, +1.26332426, +1.08800209, +1.05452311, +1.19437456, +1.92438257, +1.42765844, +1.80639517, +1.80188835, +1.66945982, +1.43477559, +1.71067059, +1.76397133, +1.35328674, +1.62448931, +1.31963706, +1.89810121, +1.76322150, +1.15715015, +1.36749327, +1.12635565, +1.08005977, +1.85237920, +1.88313961, +1.25063527, +1.71657228, +1.95433974, +1.83385539, +1.23069513, +1.53223991, +1.18322206, +1.80132663, +1.59068394, +1.69172740, +1.12441051, +1.23369968, +1.67175245, +1.95647013, +1.14383757, +1.56362307, +1.02746165, +1.82899380, +1.53953958, +1.02996027, +1.48216391, +0.238418579E-6, +0.00000000, +0.417232513E-6, -0.119209290E-6, +0.476837158E-6, -0.119209290E-6, +0.238418579E-6, -0.596046448E-7, +0.238418579E-6, +0.119209290E-6, +0.298023224E-6, -0.119209290E-6, +0.655651093E-6, +0.238418579E-6, +0.476837158E-6, +0.119209290E-6, +0.298023224E-6

62reltol = sqrt(epsilon(1._TKC))

63reltol

64+0.345266977E-3

65isClose(data, atad(1:size(data)), reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+71

72data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

73data

74+1.4333012909221527, +1.6093408109970095, +1.3024798408731231, +1.6790692920880361, +1.2922825227883621, +1.1691402861992926, +1.2715901193952786, +1.0096596928031194, +1.9527901451198955, +1.0449106301566684, +1.6356995826778631, +1.8290847963350223, +1.3838765976794190, +1.4949821327764705, +1.9901521898495087, +1.3444808941235955, +1.9669776331953401, +1.7781172168573596, +1.0391637627270560, +1.9464071415847428, +1.0735521597498243, +1.6218129084580801, +1.6656933019196694, +1.0502314279822997, +1.0224842514898704, +1.5184535206811791, +1.3526544603973085, +1.5923238401249857, +1.2761693210606404, +1.1781923482203305, +1.1754869171907680, +1.4024659322525919, +1.5448567821121053, +1.6932730950722070, +1.1988677304949822, +1.7322702265126793, +1.4403045656824927, +1.4862272454642547, +1.6410209067323842, +1.5807149676102434, +1.2392283824555268, +1.3602656996608191, +1.5066823578521018, +1.9280472389397929, +1.7661283668306911, +1.1353729407385962, +1.4088591318836028, +1.4099526859277076, +1.3686699578270198, +1.8144638529923947, +1.8914846895050710, +1.9642833409520870, +1.1353620956685115, +1.6217209090954472, +1.2193770311190870, +1.0837962463233910, +1.1386680499057820, +1.3968883341920946, +1.8058704476400078, +1.1200937865929330, +1.5961476295442489, +1.5300345953457695, +1.3686705713529550, +1.4147292681868637, +1.2499828959169195, +1.5688391686838643, +1.9596762062428561, +1.1026881351140498, +1.7194694485616266, +1.5965042601472064, +1.8453698631235693

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.4333012909221525, +1.6093408109970095, +1.3024798408731231, +1.6790692920880366, +1.2922825227883614, +1.1691402861992923, +1.2715901193952786, +1.0096596928031198, +1.9527901451198955, +1.0449106301566689, +1.6356995826778635, +1.8290847963350227, +1.3838765976794185, +1.4949821327764705, +1.9901521898495087, +1.3444808941235955, +1.9669776331953397, +1.7781172168573600, +1.0391637627270556, +1.9464071415847433, +1.0735521597498239, +1.6218129084580801, +1.6656933019196689, +1.0502314279822997, +1.0224842514898707, +1.5184535206811796, +1.3526544603973083, +1.5923238401249857, +1.2761693210606402, +1.1781923482203309, +1.1754869171907671, +1.4024659322525919, +1.5448567821121053, +1.6932730950722068, +1.1988677304949822, +1.7322702265126795, +1.4403045656824927, +1.4862272454642547, +1.6410209067323844, +1.5807149676102430, +1.2392283824555268, +1.3602656996608196, +1.5066823578521018, +1.9280472389397931, +1.7661283668306911, +1.1353729407385957, +1.4088591318836030, +1.4099526859277072, +1.3686699578270198, +1.8144638529923944, +1.8914846895050710, +1.9642833409520870, +1.1353620956685115, +1.6217209090954467, +1.2193770311190868, +1.0837962463233910, +1.1386680499057817, +1.3968883341920950, +1.8058704476400074, +1.1200937865929328, +1.5961476295442494, +1.5300345953457688, +1.3686705713529546, +1.4147292681868635, +1.2499828959169192, +1.5688391686838643, +1.9596762062428557, +1.1026881351140503, +1.7194694485616269, +1.5965042601472059, +1.8453698631235695, -0.11102230246251565E-15, +0.0000000000000000, +0.22204460492503131E-15, -0.44408920985006262E-15, +0.0000000000000000, +0.66613381477509392E-15, +0.0000000000000000, -0.11102230246251565E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.66613381477509392E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.55511151231257827E-15, +0.0000000000000000, -0.22204460492503131E-15, +0.22204460492503131E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, -0.44408920985006262E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, -0.22204460492503131E-15, +0.77715611723760958E-15, +0.0000000000000000, +0.77715611723760958E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.55511151231257827E-15, -0.55511151231257827E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, -0.44408920985006262E-15, +0.99920072216264089E-15, +0.11102230246251565E-15, +0.66613381477509392E-15

79reltol = sqrt(epsilon(1._TKC))

80reltol

81+0.14901161193847656E-7

82isClose(data, atad(1:size(data)), reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+52

89data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

90data

91+1.27018574003550639360489659661747320, +1.68390696084066266252345348240806716, +1.77727564837799691064501756539404741, +1.63117238612304449571423246039832199, +1.50694945447994675600822921797994338, +1.22031919749818281329368665238254187, +1.64400066335174965398518043613137753, +1.37773767116822541483130849461669974, +1.81968031612130197495672758010205575, +1.06270534504708723014241697894706422, +1.96113206177598839268861583647722876, +1.26616581148319213925392467202341925, +1.52864905548555934201635128909913417, +1.62818339430812398333921388224226274, +1.05557961329683884157654302123668952, +1.86852555503380582236014491895383534, +1.07627432810220392362759116154625050, +1.12307557018190043687714916538863909, +1.19679586855529132970889301170429906, +1.27897731652078666109816027891780815, +1.13995946530812424949444744688388677, +1.31766517003050737440476072565714888, +1.42129413609798310090287499862857902, +1.36203418753475514855558275292848031, +1.46735775642892390531750330372665323, +1.11616449344626840061492927719936816, +1.12829931853430346656004592529661456, +1.30664513231446171014053085939865512, +1.59000176529004324652217632281964118, +1.82991462988513202244887130268588705, +1.22357988760290331477125125373545610, +1.21429069984689657181025111375671497, +1.04000790685705561424259316864253707, +1.80015407712326685744946722578929455, +1.41376356997593191512931028519282968, +1.55500081830318428138147301652101523, +1.67682351915228478220359118192804074, +1.01671516432395344449477316166728362, +1.23021841990374917862766709408824423, +1.92548519057004691039659562312002680, +1.61166461151293412836696616662317525, +1.61729706897331063924367786297990463, +1.10540631024028061789839004946152835, +1.80606481106453832535547781673040770, +1.90700255109554069885554206219048180, +1.92223584488920478035732007687185950, +1.39868336280049237767390118146978535, +1.55637098488078221840989351548024919, +1.10975565647888065134064883641852912, +1.02191017110931638220965570924534298, +1.42015658981533155038250228086802791, +1.31686810181074374894734931071024608

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.27018574003550639360489659661747320, +1.68390696084066266252345348240806735, +1.77727564837799691064501756539404702, +1.63117238612304449571423246039832257, +1.50694945447994675600822921797994338, +1.22031919749818281329368665238254206, +1.64400066335174965398518043613137791, +1.37773767116822541483130849461669974, +1.81968031612130197495672758010205575, +1.06270534504708723014241697894706422, +1.96113206177598839268861583647722876, +1.26616581148319213925392467202341925, +1.52864905548555934201635128909913437, +1.62818339430812398333921388224226235, +1.05557961329683884157654302123668952, +1.86852555503380582236014491895383553, +1.07627432810220392362759116154625069, +1.12307557018190043687714916538863967, +1.19679586855529132970889301170429887, +1.27897731652078666109816027891780815, +1.13995946530812424949444744688388677, +1.31766517003050737440476072565714888, +1.42129413609798310090287499862857882, +1.36203418753475514855558275292848012, +1.46735775642892390531750330372665323, +1.11616449344626840061492927719936816, +1.12829931853430346656004592529661437, +1.30664513231446171014053085939865531, +1.59000176529004324652217632281964079, +1.82991462988513202244887130268588705, +1.22357988760290331477125125373545591, +1.21429069984689657181025111375671516, +1.04000790685705561424259316864253707, +1.80015407712326685744946722578929474, +1.41376356997593191512931028519282929, +1.55500081830318428138147301652101543, +1.67682351915228478220359118192804054, +1.01671516432395344449477316166728362, +1.23021841990374917862766709408824423, +1.92548519057004691039659562312002680, +1.61166461151293412836696616662317506, +1.61729706897331063924367786297990521, +1.10540631024028061789839004946152835, +1.80606481106453832535547781673040809, +1.90700255109554069885554206219048199, +1.92223584488920478035732007687185988, +1.39868336280049237767390118146978574, +1.55637098488078221840989351548024977, +1.10975565647888065134064883641852931, +1.02191017110931638220965570924534336, +1.42015658981533155038250228086802830, +1.31686810181074374894734931071024608, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.577778983316170755916793382775478196E-33

96reltol = sqrt(epsilon(1._TKC))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, atad(1:size(data)), reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+56

106data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

107data

108(+1.36382985, +0.750330746), (+1.63579321, +0.107714117), (+1.18926954, +0.618357778), (+1.25299358, +0.628122926), (+1.79030204, +0.438344002), (+1.76914346, +0.862497449), (+1.18297732, +0.941085100), (+1.48908591, +0.650392711), (+1.26521802, +0.663155198), (+1.43190837, +0.670527220), (+1.64159918, +0.313152969), (+1.89594841, +0.700847745), (+1.97733903, +0.603683770), (+1.59679699, +0.511993647), (+1.70264006, +0.811219394), (+1.93906951, +0.797203302), (+1.05435109, +0.440257013), (+1.86347044, +0.784806311), (+1.67320561, +0.912613809), (+1.54317355, +0.551694095), (+1.52470326, +0.222076178), (+1.01844573, +0.877625406), (+1.25833201, +0.112053156), (+1.35518169, +0.205975592), (+1.27954578, +0.863805473), (+1.88895738, +0.164142609), (+1.80209064, +0.615208924), (+1.34498310, +0.114480197), (+1.78571272, +0.997741818E-1), (+1.95417929, +0.626404822), (+1.69992125, +0.447108090), (+1.32554626, +0.152312994), (+1.10652530, +0.102992654), (+1.83465052, +0.519231856), (+1.82028866, +0.709739208), (+1.01478148, +0.473632395), (+1.15028107, +0.586029768), (+1.83731365, +0.193550229), (+1.89962709, +0.959112585), (+1.95318627, +0.946914792), (+1.92857265, +0.543978572), (+1.97161627, +0.950219452), (+1.29189587, +0.465228081), (+1.64353323, +0.728675783), (+1.42833972, +0.982380807), (+1.37624359, +0.710069120), (+1.27821922, +0.731479824), (+1.02517033, +0.317902803), (+1.71839607, +0.514036477), (+1.04504299, +0.753978372), (+1.92615032, +0.166083515), (+1.13392580, +0.934486985), (+1.96372199, +0.956556618), (+1.25677228, +0.388866007), (+1.32952166, +0.884617686), (+1.40636659, +0.299515903)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.36382985, +0.750330806), (+1.63579321, +0.107714191), (+1.18926954, +0.618357837), (+1.25299358, +0.628122985), (+1.79030204, +0.438344061), (+1.76914382, +0.862497330), (+1.18297732, +0.941085041), (+1.48908579, +0.650392592), (+1.26521802, +0.663155258), (+1.43190849, +0.670527220), (+1.64159918, +0.313153148), (+1.89594829, +0.700847685), (+1.97733903, +0.603684008), (+1.59679723, +0.511993825), (+1.70264006, +0.811219454), (+1.93906939, +0.797203481), (+1.05435109, +0.440257013), (+1.86347067, +0.784806252), (+1.67320585, +0.912613809), (+1.54317355, +0.551694036), (+1.52470315, +0.222076148), (+1.01844597, +0.877625346), (+1.25833201, +0.112053305), (+1.35518157, +0.205975652), (+1.27954555, +0.863805473), (+1.88895726, +0.164142728), (+1.80209041, +0.615208864), (+1.34498310, +0.114480227), (+1.78571260, +0.997741818E-1), (+1.95417905, +0.626404762), (+1.69992125, +0.447107971), (+1.32554626, +0.152312875), (+1.10652518, +0.102992743), (+1.83465052, +0.519231796), (+1.82028866, +0.709739149), (+1.01478148, +0.473632425), (+1.15028095, +0.586029828), (+1.83731389, +0.193550229), (+1.89962709, +0.959112704), (+1.95318615, +0.946914852), (+1.92857242, +0.543978631), (+1.97161615, +0.950219274), (+1.29189587, +0.465228081), (+1.64353335, +0.728675544), (+1.42833948, +0.982380807), (+1.37624383, +0.710069001), (+1.27821922, +0.731479883), (+1.02517045, +0.317902863), (+1.71839595, +0.514036417), (+1.04504335, +0.753978491), (+1.92615032, +0.166083515), (+1.13392615, +0.934486985), (+1.96372187, +0.956556678), (+1.25677252, +0.388866156), (+1.32952189, +0.884617686), (+1.40636671, +0.299515903), (+0.178813934E-6, -0.596046448E-7), (+0.417232513E-6, +0.00000000), (+0.596046448E-6, +0.119209290E-6), (+0.536441803E-6, +0.149011612E-6), (+0.357627869E-6, -0.238418579E-6), (+0.774860382E-6, -0.596046448E-7), (+0.357627869E-6, +0.149011612E-7), (+0.298023224E-6, +0.186264515E-6)

113reltol = sqrt(epsilon(1._TKC))

114reltol

115+0.345266977E-3

116isClose(data, atad(1:size(data)), reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+42

123data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

124data

125(+1.9127597679776209, +0.13684629738453502), (+1.3235644585997257, +0.93153323887656903), (+1.8163796288539280, +0.10062870184183081), (+1.7313021439444665, +0.58313187026266267), (+1.5916589584903904, +0.60701108152996364), (+1.8928355723842454, +0.50569395887252544), (+1.7029861753919788, +0.54542792511485949), (+1.0073343694932291, +0.22455325976722995), (+1.0110604822496247, +0.96410649978523044), (+1.4179212943181736, +0.88170048644362797), (+1.2983411812778924, +0.40469696025020596), (+1.7000823153438647, +0.97021084741874397), (+1.0039513452765574, +0.72350359465957248E-1), (+1.8219095636622560, +0.75757626025577329), (+1.2701667855385672, +0.77882826266416094), (+1.9005732687927057, +0.11900449812743852E-1), (+1.2758352992523139, +0.18092016505321307), (+1.8884724268152708, +0.57417894443890150), (+1.7292289806849708, +0.68622731786473135), (+1.8217138338706182, +0.96211911138551731), (+1.4882494763604666, +0.62113258958508566), (+1.8207794877786181, +0.13590297573943400), (+1.4374740437065223, +0.27549015780267594), (+1.0194312852128515, +0.95695666571778726), (+1.3813538298282824, +0.92089251389075644), (+1.8139299566372140, +0.59710778747156368), (+1.1411038617289053, +0.91380193170177793), (+1.2241911772229650, +0.68230706802652508), (+1.7792688010441979, +0.91983399543113975), (+1.8449106366836168, +0.63393886051040793), (+1.3391487023431101, +0.99757650371878559), (+1.0509884106450356, +0.35289143503942932), (+1.9402167722696673, +0.41060144382846675), (+1.6369328341237539, +0.14146365637909353), (+1.2371178038042780, +0.21502786160054810), (+1.1284642488559957, +0.66311060144786271), (+1.5278711564947445, +0.12608552682750296E-1), (+1.0597181904038759, +0.24639548122961819), (+1.5883362823976439, +0.92298932059886596E-2), (+1.2978860357856741, +0.30306117884377870), (+1.3003412237124077, +0.11918220467645979), (+1.6360463374552880, +0.64734695714872914)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.9127597679776209, +0.13684629738453502), (+1.3235644585997259, +0.93153323887656925), (+1.8163796288539273, +0.10062870184183099), (+1.7313021439444665, +0.58313187026266267), (+1.5916589584903902, +0.60701108152996364), (+1.8928355723842456, +0.50569395887252588), (+1.7029861753919786, +0.54542792511485927), (+1.0073343694932289, +0.22455325976723003), (+1.0110604822496245, +0.96410649978523066), (+1.4179212943181736, +0.88170048644362808), (+1.2983411812778924, +0.40469696025020585), (+1.7000823153438644, +0.97021084741874408), (+1.0039513452765574, +0.72350359465957526E-1), (+1.8219095636622560, +0.75757626025577351), (+1.2701667855385670, +0.77882826266416094), (+1.9005732687927055, +0.11900449812744199E-1), (+1.2758352992523139, +0.18092016505321301), (+1.8884724268152708, +0.57417894443890150), (+1.7292289806849710, +0.68622731786473090), (+1.8217138338706187, +0.96211911138551676), (+1.4882494763604666, +0.62113258958508544), (+1.8207794877786183, +0.13590297573943405), (+1.4374740437065223, +0.27549015780267566), (+1.0194312852128520, +0.95695666571778715), (+1.3813538298282826, +0.92089251389075621), (+1.8139299566372145, +0.59710778747156357), (+1.1411038617289055, +0.91380193170177737), (+1.2241911772229654, +0.68230706802652463), (+1.7792688010441977, +0.91983399543113920), (+1.8449106366836165, +0.63393886051040771), (+1.3391487023431101, +0.99757650371878492), (+1.0509884106450356, +0.35289143503942866), (+1.9402167722696673, +0.41060144382846675), (+1.6369328341237539, +0.14146365637909353), (+1.2371178038042785, +0.21502786160054804), (+1.1284642488559955, +0.66311060144786271), (+1.5278711564947443, +0.12608552682750185E-1), (+1.0597181904038759, +0.24639548122961799), (+1.5883362823976437, +0.92298932059884375E-2), (+1.2978860357856743, +0.30306117884377848), (+1.3003412237124075, +0.11918220467645962), (+1.6360463374552876, +0.64734695714872881), (+0.33306690738754696E-15, -0.16653345369377348E-15), (+0.33306690738754696E-15, -0.38857805861880479E-15), (+0.11102230246251565E-15, -0.11102230246251565E-15), (-0.22204460492503131E-15, -0.33306690738754696E-15), (+0.44408920985006262E-15, +0.55511151231257827E-16), (+0.55511151231257827E-15, -0.23592239273284576E-15), (+0.0000000000000000, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, +0.38857805861880479E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (-0.22204460492503131E-15, +0.55511151231257827E-16), (+0.0000000000000000, -0.16653345369377348E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.0000000000000000), (-0.22204460492503131E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.0000000000000000, +0.22204460492503131E-15), (+0.33306690738754696E-15, +0.49960036108132044E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (+0.44408920985006262E-15, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.72164496600635175E-15), (+0.66613381477509392E-15, +0.41633363423443370E-15)

130reltol = sqrt(epsilon(1._TKC))

131reltol

132+0.14901161193847656E-7

133isClose(data, atad(1:size(data)), reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+100

140data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

141data

142(+1.77136603397872473283163794490980740, +0.413533392474630878367096335147991051), (+1.76376020642347252149166299344580539, +0.351764731765781665680074335945646246), (+1.36674498583945797226898112171710147, +0.710617712030847140974027661945088371), (+1.56033581031458495863732740083936718, +0.588890525668950894395681480827440686), (+1.98021166240819076154574978962825065, +0.485712079994269306053301468880988091), (+1.20979868837524725004317789352430912, +0.168949195489230914106838341306262522), (+1.32925613048581796664792555871032663, +0.703293370754833836372275731164285403), (+1.06615846904651484661482030836258946, +0.323524469939048768801995096205626345), (+1.67497716236117201673095964168280920, +0.136855326446773145079168041052701711), (+1.75126303447030395043453289788068961, +0.197135219648595742789097077180414599), (+1.44333359017239380088943895253567833, +0.182836894875393872209540344004536477), (+1.51168399898567598913135847537320127, +0.464968159934186994934150156871804524), 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+0.887495198711798695860068714837916370), (+1.12111919392132895551555933672061204, +0.203482927037303879656551086869314935E-1), (+1.86816644367898211069190901178771059, +0.477532269115511535702531426256783740), (+1.42767768467750766483677270146885087, +0.764945100886139456385528432296005559), (+1.65356569253194764229543904925751988, +0.924309528915559319658999592304334611), (+1.73893840270109221447996899157575140, +0.906316084686838850327814440469269354E-1), (+1.15484416433204385965655913133400721, +0.641753519200315475748575154183923640E-2), (+1.22388342891202535801140998383311947, +0.668430295148041982228165269223139841), (+1.32437626331231278999855391712053303, +0.589870029722530442775970322145322480), (+1.19340048071982682931797199441282371, +0.980234745991164456018879739801420223), (+1.16361718334905019784765518192625945, +0.486147332395968231740394641493865626), (+1.67703383893483539970931908771699954, +0.160725703349536255828297294931646127), (+1.53602727628177900279258814643478782, +0.150319695261318869274373831931716171), (+1.73488985165452408962189768079744741, +0.941155112538915782762199328973484797E-1), (+1.71512648355670494309821474502583256, +0.292319756923684849894543251276219563), (+1.39100043277318048939651463333364206, +0.820049761778890014746162356382605759), (+1.69356801705120654569390706637269044, +0.364869247366084412949257858756202008), (+1.79791867953955450232791041140885620, +0.230475529530812509806370296003527995), (+1.32495161059546919229288138602251715, +0.509491166464811831668673117906049185), (+1.54727050262111113786619430013382373, +0.806388138191838377162155190003426978), (+1.72136551284124010206774478121411915, +0.274289206723179645850212092357676816), (+1.09954941470304230698324902092034798, +0.323623847606081866621137291978185194E-1), (+1.78775192192403129965264182286704380, +0.741356342473863444715463357621686024), (+1.65424980599617462687928250794374124, 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(+1.20597646389267146836394075119753846, +0.127494871092295450965111187322799968), (+1.93413791159975804149803704411870091, +0.307339487711747094642348013511015989), (+1.16886774314934916021502279775551339, +0.318980445285368983568703262817960790), (+1.33002249000683600929308575365062066, +0.552837460087575813008216440396696547), (+1.44161542463950291997228287851071263, +0.514335374897833707698517790360777115), (+1.59972613404842338268368085842913931, +0.437191326443050281130865571901057828)

143

144atad = getFFTI(getFFTF(data))

145atad

146(+1.77136603397872473283163794490980759, +0.413533392474630878367096335147991051), (+1.76376020642347252149166299344580500, +0.351764731765781665680074335945645958), (+1.36674498583945797226898112171710127, +0.710617712030847140974027661945088371), (+1.56033581031458495863732740083936718, +0.588890525668950894395681480827440397), (+1.98021166240819076154574978962825065, +0.485712079994269306053301468880988187), (+1.20979868837524725004317789352430854, +0.168949195489230914106838341306262017), (+1.32925613048581796664792555871032624, +0.703293370754833836372275731164285499), (+1.06615846904651484661482030836258907, +0.323524469939048768801995096205626153), (+1.67497716236117201673095964168280920, +0.136855326446773145079168041052701735), (+1.75126303447030395043453289788068980, +0.197135219648595742789097077180414262), (+1.44333359017239380088943895253567833, +0.182836894875393872209540344004536381), (+1.51168399898567598913135847537320127, +0.464968159934186994934150156871804669), 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(+1.20597646389267146836394075119753826, +0.127494871092295450965111187322800112), (+1.93413791159975804149803704411870091, +0.307339487711747094642348013511016085), (+1.16886774314934916021502279775551359, +0.318980445285368983568703262817960742), (+1.33002249000683600929308575365062047, +0.552837460087575813008216440396696740), (+1.44161542463950291997228287851071205, +0.514335374897833707698517790360777115), (+1.59972613404842338268368085842913912, +0.437191326443050281130865571901058165), (+0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.481482486096808963263994485646231830E-33, +0.553704859011330307753593658493166604E-33), (-0.674075480535532548569592279904724561E-33, -0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34), (-0.577778983316170755916793382775478196E-33, -0.288889491658085377958396691387739098E-33), (-0.770371977754894341222391177033970927E-33, -0.962964972193617926527988971292463659E-34), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-33), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-34), (-0.481482486096808963263994485646231830E-33, +0.00000000000000000000000000000000000), (-0.481482486096808963263994485646231830E-33, -0.192592994438723585305597794258492732E-33), (-0.105926146941297971918078786842171003E-32, -0.529630734706489859590393934210855013E-33), (-0.770371977754894341222391177033970927E-33, +0.00000000000000000000000000000000000), (+0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.770371977754894341222391177033970927E-33, -0.481482486096808963263994485646231830E-34), (-0.577778983316170755916793382775478196E-33, -0.144444745829042688979198345693869549E-33), (-0.770371977754894341222391177033970927E-33, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, +0.312963615962925826121596415670050689E-33), (-0.674075480535532548569592279904724561E-33, +0.481482486096808963263994485646231830E-34), (-0.770371977754894341222391177033970927E-33, -0.144444745829042688979198345693869549E-33), (-0.674075480535532548569592279904724561E-33, +0.481482486096808963263994485646231830E-34), (-0.577778983316170755916793382775478196E-33, -0.168518870133883137142398069976181140E-33), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-33), (-0.288889491658085377958396691387739098E-33, -0.457408361791968515100794761363920238E-33), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-33), (-0.192592994438723585305597794258492732E-33, -0.120370621524202240815998621411557957E-33), (-0.674075480535532548569592279904724561E-33, -0.288889491658085377958396691387739098E-33), (-0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33), (-0.866668474974256133875190074163217293E-33, -0.385185988877447170611195588516985464E-33)

147reltol = sqrt(epsilon(1._TKC))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, atad(1:size(data)), reltol = reltol)

151T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+54

157data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

158data

159+1.54697895, +1.39583647, +1.81527853, +1.88962531, +1.43981206, +1.58826423, +1.30705881, +1.81809020, +1.90542746, +1.55842233, +1.41315293, +1.12542391, +1.32804918, +1.29082155, +1.17871404, +1.68382359, +1.53919411, +1.92406249, +1.65280581, +1.80492580, +1.43579984, +1.08037710, +1.58095849, +1.27039087, +1.52953041, +1.90091109, +1.42502558, +1.12440264, +1.04122961, +1.36292100, +1.33317709, +1.46422088, +1.44915760, +1.21438265, +1.19184995, +1.95782721, +1.91819918, +1.07510018, +1.91614509, +1.35071778, +1.88372290, +1.89132106, +1.37358928, +1.45421982, +1.66959953, +1.89491689, +1.49396670, +1.73484337, +1.21487927, +1.02720118, +1.02478635, +1.71939540, +1.11266625, +1.82238674

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.54697895, +1.39583623, +1.81527853, +1.88962543, +1.43981206, +1.58826411, +1.30705881, +1.81808996, +1.90542746, +1.55842221, +1.41315281, +1.12542391, +1.32804942, +1.29082131, +1.17871416, +1.68382335, +1.53919423, +1.92406225, +1.65280581, +1.80492568, +1.43579984, +1.08037710, +1.58095849, +1.27039075, +1.52953053, +1.90091085, +1.42502546, +1.12440252, +1.04122961, +1.36292064, +1.33317697, +1.46422064, +1.44915771, +1.21438229, +1.19185019, +1.95782721, +1.91819918, +1.07510006, +1.91614509, +1.35071754, +1.88372302, +1.89132082, +1.37358916, +1.45421982, +1.66959953, +1.89491653, +1.49396694, +1.73484302, +1.21487939, +1.02720118, +1.02478647, +1.71939540, +1.11266637, +1.82238650, +0.119209290E-6, +0.596046448E-7, +0.298023224E-6, +0.178813934E-6, -0.178813934E-6, +0.178813934E-6, +0.357627869E-6, -0.119209290E-6, -0.119209290E-6, +0.00000000

164reltol = sqrt(epsilon(1._TKC))

165reltol

166+0.345266977E-3

167isClose(data, atad(1:size(data)), reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+99

174data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

175data

176+1.1021458516215104, +1.8266810551982779, +1.9241826872867263, +1.5366621399384530, +1.4228953831122988, +1.7345634959216036, +1.2509661131385483, +1.1960417414952096, +1.7900209249508841, +1.7952581539424053, +1.0067138982811636, +1.8502309016199661, +1.2654154322053315, +1.6826495065596283, +1.3100006114370486, +1.9659154379853838, +1.3829205230431754, +1.9758085311004778, +1.1024104764629712, +1.5267492454183911, +1.6675303651313771, +1.3286044271700466, +1.6387983536851847, +1.0704459347440265, +1.1466700640440630, +1.6071634932944270, +1.9931866048202895, +1.0826930308000442, +1.5050986953523906, +1.8606140490930589, +1.9430776904779392, +1.1464008850178802, +1.8929944052692558, +1.8451579118421275, +1.7175117473612882, +1.3950393888869277, +1.8997183693634625, +1.4951544109252781, +1.8328223978766134, +1.2540592467053275, +1.3236882406296089, +1.2415484481046062, +1.4765530526024406, +1.9283920113385538, +1.2034719474800912, +1.1974380470334849, +1.0311017489658671, +1.8505331777874172, +1.5419204518710385, +1.8439043075713997, +1.3433064434852640, +1.1006514537918790, +1.9178585049615946, +1.4324099487037900, +1.4231035956596583, +1.2930893870766034, +1.4022119646174354, +1.6711748815580680, +1.1460164460510038, +1.9078938033619717, +1.6625459705973227, +1.3367521751785905, +1.8875486534047095, +1.5487244445450350, +1.6818153170355377, +1.6617724070767039, +1.0536045712667941, +1.0996630816571367, +1.7125752578485471, +1.6452726249556635, +1.5094127938899666, +1.7470955696134376, +1.2519269872446168, +1.2007948700588928, +1.2405839119763424, +1.2235685914187848, +1.2984761553945814, +1.3401992015438351, +1.2838474809730263, +1.7727066804834886, +1.2644340599812556, +1.0747872032922481, +1.7756017499736991, +1.4851669180692175, +1.5048899999530740, +1.3489152274037575, +1.0980971792804342, +1.8925151853652729, +1.3104736097193421, +1.0978382138383562, +1.4439605919176035, +1.8101563829426981, +1.9284043950163308, +1.4959509575938779, +1.7231981681519659, +1.4041426010160540, +1.6955959835650196, +1.7706981555598216, +1.4887829910253600

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.1021458516215104, +1.8266810551982782, +1.9241826872867265, +1.5366621399384535, +1.4228953831122984, +1.7345634959216041, +1.2509661131385479, +1.1960417414952103, +1.7900209249508841, +1.7952581539424060, +1.0067138982811634, +1.8502309016199665, +1.2654154322053308, +1.6826495065596290, +1.3100006114370482, +1.9659154379853843, +1.3829205230431751, +1.9758085311004783, +1.1024104764629710, +1.5267492454183909, +1.6675303651313762, +1.3286044271700475, +1.6387983536851845, +1.0704459347440265, +1.1466700640440630, +1.6071634932944274, +1.9931866048202891, +1.0826930308000449, +1.5050986953523895, +1.8606140490930594, +1.9430776904779383, +1.1464008850178811, +1.8929944052692558, +1.8451579118421277, +1.7175117473612880, +1.3950393888869281, +1.8997183693634625, +1.4951544109252783, +1.8328223978766134, +1.2540592467053271, +1.3236882406296093, +1.2415484481046062, +1.4765530526024406, +1.9283920113385538, +1.2034719474800912, +1.1974380470334851, +1.0311017489658676, +1.8505331777874172, +1.5419204518710392, +1.8439043075713997, +1.3433064434852644, +1.1006514537918788, +1.9178585049615944, +1.4324099487037900, +1.4231035956596585, +1.2930893870766031, +1.4022119646174358, +1.6711748815580683, +1.1460164460510041, +1.9078938033619712, +1.6625459705973225, +1.3367521751785905, +1.8875486534047092, +1.5487244445450346, +1.6818153170355377, +1.6617724070767039, +1.0536045712667941, +1.0996630816571367, +1.7125752578485471, +1.6452726249556637, +1.5094127938899669, +1.7470955696134371, +1.2519269872446168, +1.2007948700588931, +1.2405839119763427, +1.2235685914187844, +1.2984761553945809, +1.3401992015438355, +1.2838474809730265, +1.7727066804834881, +1.2644340599812554, +1.0747872032922479, +1.7756017499736989, +1.4851669180692169, +1.5048899999530738, +1.3489152274037577, +1.0980971792804344, +1.8925151853652720, +1.3104736097193423, +1.0978382138383562, +1.4439605919176035, +1.8101563829426974, +1.9284043950163301, +1.4959509575938776, +1.7231981681519664, +1.4041426010160531, +1.6955959835650201, +1.7706981555598216, +1.4887829910253600, -0.33306690738754696E-15, +0.33306690738754696E-15, +0.11102230246251565E-14, +0.11102230246251565E-14, +0.0000000000000000, +0.11102230246251565E-15, +0.0000000000000000, +0.33306690738754696E-15, -0.44408920985006262E-15, +0.11102230246251565E-15, +0.77715611723760958E-15, +0.77715611723760958E-15, +0.77715611723760958E-15, +0.0000000000000000, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.0000000000000000, +0.22204460492503131E-15, +0.99920072216264089E-15, +0.88817841970012523E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.88817841970012523E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.14432899320127035E-14, +0.99920072216264089E-15, +0.88817841970012523E-15

181reltol = sqrt(epsilon(1._TKC))

182reltol

183+0.14901161193847656E-7

184isClose(data, atad(1:size(data)), reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+55

191data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

192data

193+1.18847434318212597941297335130664329, +1.88952702092279254881422448080236154, +1.18981240262492833858226817399669606, +1.26316796137416484471677279854851408, +1.17271757167199144240994616236338419, +1.53373168594706874155784867946793301, +1.41337339042399303861105804260027144, +1.85092310210921713305146271544564800, +1.95246262019731783642791219348594921, +1.74767708015081477279106568676270217, +1.17437895750465122802064365205860875, +1.79187266384384056503703543100356554, +1.54791707504612538429733945574866303, +1.88745040206331247312221360764770572, +1.48832010185831823724194835499836483, +1.02793958359238691109032744466028525, +1.06217936072608464354419285415482416, +1.58071882572663605383565438295739477, +1.49790261090272975844902806661976326, +1.73356673134307461275827492395165590, +1.70679914063048908909013201469532410, +1.14628373065040378096597812590106321, +1.18047386582461414235571407561060912, +1.32439866440976476521485438911992819, +1.28599831566945845365862994207420816, +1.19924516979048166365859578269947198, +1.69619469523872301779972893812816570, +1.38791791046769657870280569748468458, +1.61481954694193284815899765100403534, +1.19316598157760992578379845711459209, +1.92260327070645592288646726623228413, +1.44473687379470778064027441720385590, +1.03724909979780664455301400305300783, +1.18569583359110986312760474066340352, +1.71352336302734352863281753936483487, +1.72159982063265500799947327161494770, +1.62490029965610900474269746868738731, +1.75046362165633732433226734115390362, +1.50139007828935306028025870941287095, +1.07837259876301148875398061865768208, +1.70362425141685912421167575491268153, +1.30049286721494125966332080989141164, +1.19711016039217749330941946811911458, +1.69733607639354457319321331361647341, +1.69016272715386018587499716636261490, +1.12420863673978740481686029759739274, +1.15554327971416147565539643220572353, +1.20852351689033175598537100604199074, +1.94179605382920664406148734453595746, +1.04574582993575694846511418208064692, +1.67836727694441767504334979830694796, +1.01503089795891241809658065774415524, +1.29460170584101698007768687219707565, +1.74744569141412500762132102204807470, +1.03376839435170575750538333630523155

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.18847434318212597941297335130664310, +1.88952702092279254881422448080236154, +1.18981240262492833858226817399669586, +1.26316796137416484471677279854851427, +1.17271757167199144240994616236338400, +1.53373168594706874155784867946793301, +1.41337339042399303861105804260027124, +1.85092310210921713305146271544564819, +1.95246262019731783642791219348594902, +1.74767708015081477279106568676270198, +1.17437895750465122802064365205860913, +1.79187266384384056503703543100356554, +1.54791707504612538429733945574866323, +1.88745040206331247312221360764770572, +1.48832010185831823724194835499836483, +1.02793958359238691109032744466028525, +1.06217936072608464354419285415482396, +1.58071882572663605383565438295739457, +1.49790261090272975844902806661976307, +1.73356673134307461275827492395165570, +1.70679914063048908909013201469532371, +1.14628373065040378096597812590106340, +1.18047386582461414235571407561060893, +1.32439866440976476521485438911992838, +1.28599831566945845365862994207420778, +1.19924516979048166365859578269947160, +1.69619469523872301779972893812816570, +1.38791791046769657870280569748468458, +1.61481954694193284815899765100403515, +1.19316598157760992578379845711459209, +1.92260327070645592288646726623228413, +1.44473687379470778064027441720385628, +1.03724909979780664455301400305300764, +1.18569583359110986312760474066340352, +1.71352336302734352863281753936483506, +1.72159982063265500799947327161494770, +1.62490029965610900474269746868738712, +1.75046362165633732433226734115390382, +1.50139007828935306028025870941287095, +1.07837259876301148875398061865768208, +1.70362425141685912421167575491268134, +1.30049286721494125966332080989141145, +1.19711016039217749330941946811911516, +1.69733607639354457319321331361647360, +1.69016272715386018587499716636261490, +1.12420863673978740481686029759739235, +1.15554327971416147565539643220572334, +1.20852351689033175598537100604199113, +1.94179605382920664406148734453595707, +1.04574582993575694846511418208064673, +1.67836727694441767504334979830694796, +1.01503089795891241809658065774415505, +1.29460170584101698007768687219707488, +1.74744569141412500762132102204807470, +1.03376839435170575750538333630523136, +0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33, -0.674075480535532548569592279904724561E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34

198reltol = sqrt(epsilon(1._TKC))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, atad(1:size(data)), reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+62

208data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

209data

210(+1.51652706, +0.482590616), (+1.56029499, +0.411288619), (+1.55151916, +0.285504818), (+1.67857540, +0.462108850E-2), (+1.72729063, +0.740353286), (+1.95186949, +0.272501349), (+1.73162699, +0.710884213), (+1.42876887, +0.918576479), (+1.65129721, +0.553070486), (+1.30515814, +0.641406715), (+1.71033168, +0.430020213), (+1.85672045, +0.267085612), (+1.61707330, +0.665971100), (+1.84268570, +0.804675698), (+1.04927480, +0.620370626), (+1.16203225, +0.494422793), (+1.89139366, +0.383101761), (+1.03950465, +0.258514822), (+1.14416337, +0.658383548), (+1.06350279, +0.482719064), (+1.41546059, +0.592269003), (+1.10515690, +0.740919352), (+1.04703474, +0.203282952), (+1.19767880, +0.227644324), (+1.18141484, +0.665914237), (+1.38568783, +0.764083445), (+1.68984842, +0.935143590), (+1.93178487, +0.356292605), (+1.08891177, +0.387469769), (+1.40112090, +0.776192844), (+1.53309679, +0.101540327), (+1.55174994, +0.105202615), (+1.84392989, +0.322075367), (+1.61822796, +0.261630118), (+1.61638331, +0.513299406), (+1.24565625, +0.897052288E-1), (+1.92166102, +0.171889782), (+1.90850353, +0.117935359), (+1.46666598, +0.784668148), (+1.77687883, +0.997507572E-1), (+1.21269643, +0.434102118), (+1.19327211, +0.539195418), (+1.08708012, +0.264330506E-1), (+1.21877909, +0.551500916), (+1.47010827, +0.438292623), (+1.81572556, +0.620978594), (+1.23158741, +0.136497021E-1), (+1.25903988, +0.689544559), (+1.25344718, +0.617824435), (+1.10986733, +0.490946412), (+1.20027375, +0.758420050), (+1.49764395, +0.205551088), (+1.16046739, +0.341709256), (+1.19971466, +0.623500884), (+1.47154903, +0.930131435), (+1.08974743, +0.760681331), (+1.48758590, +0.266270459), (+1.75660491, +0.917109191), (+1.16235745, +0.340722620), (+1.61337745, +0.733040094), (+1.33579373, +0.856091678), (+1.15259111, +0.545320511)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.51652706, +0.482590556), (+1.56029510, +0.411288738), (+1.55151880, +0.285504878), (+1.67857504, +0.462118164E-2), (+1.72729063, +0.740353346), (+1.95186949, +0.272501349), (+1.73162675, +0.710884094), (+1.42876887, +0.918576419), (+1.65129709, +0.553070486), (+1.30515826, +0.641406655), (+1.71033156, +0.430020213), (+1.85672069, +0.267085552), (+1.61707342, +0.665971160), (+1.84268546, +0.804675758), (+1.04927480, +0.620370626), (+1.16203237, +0.494422853), (+1.89139366, +0.383101761), (+1.03950477, +0.258514851), (+1.14416313, +0.658383608), (+1.06350303, +0.482719183), (+1.41546047, +0.592268944), (+1.10515690, +0.740919232), (+1.04703462, +0.203282982), (+1.19767880, +0.227644473), (+1.18141484, +0.665914178), (+1.38568783, +0.764083445), (+1.68984818, +0.935143471), (+1.93178487, +0.356292635), (+1.08891189, +0.387469739), (+1.40112066, +0.776192904), (+1.53309655, +0.101540349), (+1.55174994, +0.105202667), (+1.84392989, +0.322075367), (+1.61822796, +0.261630177), (+1.61638319, +0.513299406), (+1.24565625, +0.897053480E-1), (+1.92166090, +0.171889812), (+1.90850353, +0.117935449), (+1.46666598, +0.784668207), (+1.77687883, +0.997508168E-1), (+1.21269655, +0.434102058), (+1.19327223, +0.539195418), (+1.08708012, +0.264331251E-1), (+1.21877933, +0.551500797), (+1.47010839, +0.438292742), (+1.81572533, +0.620978653), (+1.23158729, +0.136498213E-1), (+1.25903964, +0.689544618), (+1.25344706, +0.617824495), (+1.10986733, +0.490946442), (+1.20027351, +0.758419991), (+1.49764395, +0.205551028), (+1.16046727, +0.341709226), (+1.19971466, +0.623500824), (+1.47154915, +0.930131555), (+1.08974743, +0.760681391), (+1.48758578, +0.266270459), (+1.75660491, +0.917109191), (+1.16235733, +0.340722769), (+1.61337781, +0.733039975), (+1.33579385, +0.856091619), (+1.15259099, +0.545320511), (+0.00000000, +0.670552254E-7), (+0.357627869E-6, +0.126659870E-6)

215reltol = sqrt(epsilon(1._TKC))

216reltol

217+0.345266977E-3

218isClose(data, atad(1:size(data)), reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+9

225data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

226data

227(+1.8949871577923587, +0.29073337879877947), (+1.8134913463645892, +0.81618116643619298), (+1.1721372744549805, +0.52271049534802450), (+1.1579762282334070, +0.28727715806449727E-1), (+1.4136555343059629, +0.24483558757166790), (+1.3224899776215469, +0.88538073513875104E-1), (+1.7415803786327437, +0.52416205859470444), (+1.6966971567309956, +0.44019128292823972), (+1.5253744298538967, +0.13967901414540240)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.8949871577923587, +0.29073337879877947), (+1.8134913463645890, +0.81618116643619310), (+1.1721372744549803, +0.52271049534802461), (+1.1579762282334065, +0.28727715806449783E-1), (+1.4136555343059629, +0.24483558757166768), (+1.3224899776215469, +0.88538073513874965E-1), (+1.7415803786327437, +0.52416205859470399), (+1.6966971567309952, +0.44019128292823928), (+1.5253744298538967, +0.13967901414540240), (+0.0000000000000000, -0.16653345369377348E-15), (+0.44408920985006262E-15, +0.0000000000000000), (+0.44408920985006262E-15, -0.11102230246251565E-15), (+0.0000000000000000, +0.13877787807814457E-15), (+0.0000000000000000, +0.13877787807814457E-15), (+0.0000000000000000, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.38857805861880479E-15)

232reltol = sqrt(epsilon(1._TKC))

233reltol

234+0.14901161193847656E-7

235isClose(data, atad(1:size(data)), reltol = reltol)

236T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+67

242data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

243data

244(+1.47346937307314634911691906787794951, +0.260067410523585161712393699450565364), (+1.44411598746118295319733091107616805, +0.803940269457966554459372702226384291), (+1.90652671915119914158814798791898574, +0.151208504650838633039578468763035064), (+1.73204154883808369442326116371035683, +0.108100910622636561389978499952552316), (+1.55183013218688490501486242352547460, +0.556150403047309475896240684278951111), (+1.86403674301422162675880996872623001, +0.690938438235759633038469080546748497), (+1.41071992943525637252415016787822728, +0.151942851013717830165769264084771446), (+1.98430382128011668783162700518315841, +0.136740687777780740372774481287545301E-1), (+1.56778356815847221377333043083132730, +0.105346617152634287839258949968736861), (+1.84963854781881841616315736118946293, +0.986564187786449955449402535901220846), (+1.74909911850709754842615584835356269, +0.271502755370279302269213739809760319), (+1.26423342533668340540977887044743884, 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245

246atad = getFFTI(getFFTF(data))

247atad

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-0.385185988877447170611195588516985464E-33), (-0.288889491658085377958396691387739098E-33, -0.433334237487128066937595037081608647E-33), (-0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.637964294078271876324792693481257174E-33), (-0.192592994438723585305597794258492732E-33, -0.433334237487128066937595037081608647E-33), (-0.577778983316170755916793382775478196E-33, -0.577778983316170755916793382775478196E-33)

249reltol = sqrt(epsilon(1._TKC))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, atad(1:size(data)), reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+47

259data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

260data

261+1.41322994, +1.97214127, +1.20311522, +1.72567809, +1.73645818, +1.15283227, +1.81449151, +1.53743887, +1.15281177, +1.05944467, +1.06875825, +1.26251328, +1.73053885, +1.08708453, +1.16779780, +1.24723601, +1.10472596, +1.23901081, +1.67074955, +1.81404495, +1.94404364, +1.65275097, +1.23831046, +1.83118749, +1.40391982, +1.30855668, +1.07489693, +1.46609926, +1.71740913, +1.25445437, +1.27564478, +1.62622225, +1.34503317, +1.18182325, +1.49610662, +1.82557917, +1.01289129, +1.10223961, +1.76181793, +1.69086289, +1.95766962, +1.73106551, +1.78070712, +1.83549142, +1.36744857, +1.94679546, +1.91193271

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.41323006, +1.97214115, +1.20311522, +1.72567797, +1.73645842, +1.15283215, +1.81449127, +1.53743875, +1.15281177, +1.05944443, +1.06875825, +1.26251340, +1.73053873, +1.08708453, +1.16779768, +1.24723589, +1.10472608, +1.23901057, +1.67074955, +1.81404483, +1.94404364, +1.65275097, +1.23831046, +1.83118749, +1.40391982, +1.30855668, +1.07489681, +1.46609926, +1.71740890, +1.25445414, +1.27564478, +1.62622237, +1.34503329, +1.18182313, +1.49610662, +1.82557893, +1.01289141, +1.10223949, +1.76181817, +1.69086277, +1.95766950, +1.73106527, +1.78070712, +1.83549142, +1.36744845, +1.94679523, +1.91193283, +0.357627869E-6, +0.00000000, +0.00000000, -0.119209290E-6, +0.357627869E-6, +0.178813934E-6, +0.00000000, +0.119209290E-6, +0.119209290E-6, +0.238418579E-6, +0.238418579E-6, +0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.596046448E-7, +0.00000000, +0.298023224E-6

266reltol = sqrt(epsilon(1._TKC))

267reltol

268+0.345266977E-3

269isClose(data, atad(1:size(data)), reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+46

276data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

277data

278+1.0873407639311894, +1.8173652056064107, +1.9748241683518162, +1.8354894009007718, +1.8568067393335714, +1.8718783525075908, +1.5324259665755622, +1.8877131167487122, +1.8100663357984579, +1.7159389516016514, +1.3738803944282227, +1.4409439811460625, +1.9632157481975443, +1.0101528250977410, +1.9673760745902422, +1.1536964473012812, +1.9069686010601394, +1.8871417206930343, +1.9255071796786936, +1.2374010618798943, +1.0469128292710304, +1.2129898720770527, +1.5404397258530182, +1.2362928525557750, +1.7351871756880048, +1.4755001962367011, +1.2113885999444078, +1.8790009013482640, +1.3923697655133118, +1.7882468107352549, +1.5371113631410760, +1.4460051141671997, +1.1994345087116454, +1.8912184159777712, +1.8024954924425498, +1.5202584346746506, +1.8794355877097244, +1.6617177903290630, +1.3416486041742344, +1.5016442592098009, +1.5075914642267232, +1.8527320075291733, +1.7924909160405833, +1.3647838733690774, +1.9405797004677998, +1.6970039616639803

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.0873407639311896, +1.8173652056064109, +1.9748241683518160, +1.8354894009007714, +1.8568067393335712, +1.8718783525075910, +1.5324259665755617, +1.8877131167487113, +1.8100663357984579, +1.7159389516016512, +1.3738803944282225, +1.4409439811460620, +1.9632157481975441, +1.0101528250977405, +1.9673760745902418, +1.1536964473012810, +1.9069686010601397, +1.8871417206930345, +1.9255071796786938, +1.2374010618798938, +1.0469128292710301, +1.2129898720770527, +1.5404397258530182, +1.2362928525557746, +1.7351871756880048, +1.4755001962367011, +1.2113885999444083, +1.8790009013482638, +1.3923697655133114, +1.7882468107352547, +1.5371113631410755, +1.4460051141671992, +1.1994345087116458, +1.8912184159777714, +1.8024954924425498, +1.5202584346746504, +1.8794355877097242, +1.6617177903290627, +1.3416486041742339, +1.5016442592098005, +1.5075914642267230, +1.8527320075291733, +1.7924909160405831, +1.3647838733690767, +1.9405797004677996, +1.6970039616639800, +0.44408920985006262E-15, -0.44408920985006262E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.44408920985006262E-15, +0.0000000000000000, +0.22204460492503131E-15, -0.22204460492503131E-15, +0.88817841970012523E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, +0.44408920985006262E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.66613381477509392E-15, +0.33306690738754696E-15

283reltol = sqrt(epsilon(1._TKC))

284reltol

285+0.14901161193847656E-7

286isClose(data, atad(1:size(data)), reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+32

293data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

294data

295+1.03874423035530247058786748999021144, +1.30193679987334812034576409188199434, +1.87197641797023700022741474657857465, +1.48908938528874699990319449399176259, +1.93961387981669597713938231610108111, +1.47968715397243520322118891966960717, +1.22269632187023346734580714015949985, +1.20393347190413443477751087373515215, +1.55186041830562622157941049667547034, +1.56261633692455964786756062619878920, +1.78347615809632886021769992213294749, +1.28161641628079454713690830935753195, +1.77092260642305519004781344517730907, +1.58272008362545206198399721288576623, +1.97217800430726637446576664350193491, +1.57263738613002490828416530046727413, +1.12515580330814712843626600696632552, +1.19807461764701263615851952964148910, +1.63848895331827375947079168185053962, +1.74912186091803102193238179416745716, +1.22371603495240133728800935675786517, +1.50014629506215690198581279368308606, +1.12958261101208790899518711901991159, +1.45360063453543627324931711989464194, +1.77798085735331014059217956515812292, +1.96845662919139504196802399140061871, +1.27539460619118444884551803683725608, +1.98801580985340251580760938872278311, +1.70996535694623685340585285390197121, +1.15992075279258667627759369553442182, +1.01874472628597264319563869929550362, +1.24802223357794502058437829771383205

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.03874423035530247058786748999021163, +1.30193679987334812034576409188199415, +1.87197641797023700022741474657857465, +1.48908938528874699990319449399176239, +1.93961387981669597713938231610108111, +1.47968715397243520322118891966960698, +1.22269632187023346734580714015949985, +1.20393347190413443477751087373515158, +1.55186041830562622157941049667547072, +1.56261633692455964786756062619878881, +1.78347615809632886021769992213294788, +1.28161641628079454713690830935753157, +1.77092260642305519004781344517730926, +1.58272008362545206198399721288576642, +1.97217800430726637446576664350193511, +1.57263738613002490828416530046727394, +1.12515580330814712843626600696632571, +1.19807461764701263615851952964148891, +1.63848895331827375947079168185053962, +1.74912186091803102193238179416745716, +1.22371603495240133728800935675786517, +1.50014629506215690198581279368308587, +1.12958261101208790899518711901991140, +1.45360063453543627324931711989464155, +1.77798085735331014059217956515812331, +1.96845662919139504196802399140061852, +1.27539460619118444884551803683725608, +1.98801580985340251580760938872278311, +1.70996535694623685340585285390197140, +1.15992075279258667627759369553442182, +1.01874472628597264319563869929550343, +1.24802223357794502058437829771383185

300reltol = sqrt(epsilon(1._TKC))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, atad(1:size(data)), reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+39

310data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

311data

312(+1.94596457, +0.305849493), (+1.30602801, +0.540139019), (+1.71141219, +0.771190286), (+1.82671309, +0.741304517), (+1.96173835, +0.330922902), (+1.07575631, +0.278888524), (+1.13286519, +0.788778365), (+1.13153815, +0.142158389), (+1.10311770, +0.503663778), (+1.90832233, +0.783597231E-1), (+1.34035993, +0.793996692), (+1.62462807, +0.951974034), (+1.05168140, +0.394192338E-1), (+1.57530403, +0.696651936), (+1.64511371, +0.311606228), (+1.47460306, +0.816239715E-1), (+1.97460437, +0.940808654), (+1.99633241, +0.467776299), (+1.71268129, +0.214512050), (+1.36720133, +0.219941854), (+1.51354837, +0.753873587), (+1.48722017, +0.534703195), (+1.65069187, +0.951886415), (+1.61237049, +0.911609828), (+1.73848033, +0.430583596), (+1.50110590, +0.299438894), (+1.99150014, +0.662734509E-1), (+1.67246819, +0.931095243), (+1.23767495, +0.706329942), (+1.10150647, +0.746807158), (+1.50574565, +0.183477402E-1), (+1.28437209, +0.994126976), (+1.08758163, +0.654974043), (+1.11343408, +0.763504922), (+1.66687608, +0.174238026), (+1.39972711, +0.326942801E-1), (+1.77333188, +0.181011677), (+1.42183852, +0.546874106), (+1.42927670, +0.764051199)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.94596457, +0.305849582), (+1.30602789, +0.540138960), (+1.71141207, +0.771190166), (+1.82671273, +0.741304278), (+1.96173847, +0.330922961), (+1.07575643, +0.278888494), (+1.13286519, +0.788778305), (+1.13153791, +0.142158255), (+1.10311770, +0.503664017), (+1.90832210, +0.783599168E-1), (+1.34035993, +0.793996692), (+1.62462795, +0.951973915), (+1.05168152, +0.394194871E-1), (+1.57530379, +0.696652174), (+1.64511371, +0.311606288), (+1.47460294, +0.816241354E-1), (+1.97460449, +0.940808594), (+1.99633217, +0.467776239), (+1.71268106, +0.214511931), (+1.36720121, +0.219941765), (+1.51354849, +0.753873527), (+1.48722029, +0.534703374), (+1.65069199, +0.951886415), (+1.61237025, +0.911609530), (+1.73848009, +0.430583596), (+1.50110567, +0.299438894), (+1.99149990, +0.662736446E-1), (+1.67246783, +0.931095123), (+1.23767471, +0.706329942), (+1.10150623, +0.746807098), (+1.50574541, +0.183478519E-1), (+1.28437197, +0.994127035), (+1.08758163, +0.654974103), (+1.11343408, +0.763504863), (+1.66687620, +0.174237996), (+1.39972723, +0.326943398E-1), (+1.77333200, +0.181011781), (+1.42183840, +0.546874166), (+1.42927694, +0.764051199), (+0.238418579E-6, +0.447034836E-7), (+0.00000000, -0.149011612E-6), (+0.298023224E-6, -0.108033419E-6), (+0.298023224E-6, -0.298023224E-7), (+0.357627869E-6, +0.596046448E-7), (+0.596046448E-7, -0.134110451E-6), (+0.178813934E-6, -0.119209290E-6), (+0.596046448E-7, +0.447034836E-7), (+0.298023224E-6, -0.745058060E-7), (-0.119209290E-6, +0.596046448E-7), (+0.178813934E-6, +0.134110451E-6), (+0.238418579E-6, +0.149011612E-6), (+0.119209290E-6, +0.178813934E-6), (+0.119209290E-6, +0.596046448E-7), (+0.178813934E-6, -0.894069672E-7), (+0.178813934E-6, +0.894069672E-7), (+0.178813934E-6, +0.119209290E-6), (+0.178813934E-6, +0.596046448E-7), (+0.357627869E-6, +0.149011612E-7), (+0.238418579E-6, +0.745058060E-7), (+0.357627869E-6, +0.178813934E-6), (+0.178813934E-6, -0.596046448E-7), (+0.298023224E-6, +0.00000000), (+0.119209290E-6, -0.670552254E-7), (+0.00000000, +0.00000000)

317reltol = sqrt(epsilon(1._TKC))

318reltol

319+0.345266977E-3

320isClose(data, atad(1:size(data)), reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+42

327data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

328data

329(+1.7214652055472270, +0.68475543513835591), (+1.0915814383869742, +0.32818740075932451), (+1.2045312489296123, +0.46022153989229664), (+1.4613106048917825, +0.40430797652077088), (+1.6098688419154823, +0.76943951005555145), (+1.3544338803028722, +0.41864706320443590E-1), (+1.7545382801723233, +0.68599529105463208), (+1.2470722524808617, +0.88808435688912502), (+1.7182640464978873, +0.64264084046187031), (+1.5548125392113215, +0.44529402299065923), (+1.4149841497636579, +0.55312138214777251), (+1.9942024160271559, +0.23720372812488755), (+1.5146185664502116, +0.27789620131726689), (+1.6615962023481377, +0.72384078492171411), (+1.8926151879280881, +0.61047192160037556), (+1.8550087903505483, +0.86354298750613367), (+1.0195436287066959, +0.42203554465377691), (+1.8315942455832053, +0.45728855851257399), (+1.0625974868233534, +0.60319736523710477E-1), (+1.7532983818533834, +0.26541883916343234), (+1.9876262589920553, +0.26545497910871740), (+1.0204443624239807, +0.26775845230728823), (+1.6526165152471024, +0.45549305973898924), (+1.2760007647479581, +0.82288785164954659), (+1.5017218140968454, +0.79059579065251595), (+1.9435345314588459, +0.68430194856814508), (+1.5841998896814116, +0.26379351409842788), (+1.8089652611691664, +0.89830123154948482), (+1.5264793375130461, +0.55348585994491073), (+1.5887604216709628, +0.15694900415304169), (+1.3759489018347986, +0.33449540899722330), (+1.3627250708929399, +0.15436272787509020), (+1.1008431072536982, +0.48407707174092440), (+1.0164456005257716, +0.92240158995183519), (+1.8429524143234139, +0.98976737628694023), (+1.5467759266785954, +0.36400703869877493), (+1.5462877939219886, +0.27816626098757480), (+1.5353632461420441, +0.74093900214724140), (+1.3384932968871093, +0.54924875024209263), (+1.3143066878217211, +0.73187488265703748), (+1.4426244264676642, +0.85113698484215461E-1), (+1.6813338016665500, +0.12170835227542698E-1)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.7214652055472275, +0.68475543513835602), (+1.0915814383869744, +0.32818740075932484), (+1.2045312489296123, +0.46022153989229703), (+1.4613106048917823, +0.40430797652077122), (+1.6098688419154823, +0.76943951005555133), (+1.3544338803028724, +0.41864706320443590E-1), (+1.7545382801723231, +0.68599529105463231), (+1.2470722524808615, +0.88808435688912546), (+1.7182640464978873, +0.64264084046187064), (+1.5548125392113217, +0.44529402299065962), (+1.4149841497636579, +0.55312138214777284), (+1.9942024160271554, +0.23720372812488805), (+1.5146185664502112, +0.27789620131726722), (+1.6615962023481377, +0.72384078492171433), (+1.8926151879280875, +0.61047192160037556), (+1.8550087903505477, +0.86354298750613412), (+1.0195436287066961, +0.42203554465377702), (+1.8315942455832053, +0.45728855851257399), (+1.0625974868233539, +0.60319736523710435E-1), (+1.7532983818533829, +0.26541883916343190), (+1.9876262589920555, +0.26545497910871740), (+1.0204443624239810, +0.26775845230728812), (+1.6526165152471022, +0.45549305973898918), (+1.2760007647479581, +0.82288785164954636), (+1.5017218140968460, +0.79059579065251573), (+1.9435345314588464, +0.68430194856814497), (+1.5841998896814116, +0.26379351409842744), (+1.8089652611691660, +0.89830123154948416), (+1.5264793375130457, +0.55348585994491040), (+1.5887604216709628, +0.15694900415304147), (+1.3759489018347981, +0.33449540899722285), (+1.3627250708929395, +0.15436272787508987), (+1.1008431072536986, +0.48407707174092440), (+1.0164456005257714, +0.92240158995183519), (+1.8429524143234142, +0.98976737628693967), (+1.5467759266785952, +0.36400703869877460), (+1.5462877939219886, +0.27816626098757480), (+1.5353632461420441, +0.74093900214724173), (+1.3384932968871095, +0.54924875024209219), (+1.3143066878217209, +0.73187488265703715), (+1.4426244264676642, +0.85113698484215350E-1), (+1.6813338016665498, +0.12170835227542587E-1), (+0.77715611723760958E-15, -0.33306690738754696E-15), (+0.33306690738754696E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, -0.24980018054066022E-15), (-0.11102230246251565E-15, -0.44408920985006262E-15), (+0.44408920985006262E-15, +0.0000000000000000), (+0.22204460492503131E-15, -0.33306690738754696E-15), (+0.22204460492503131E-15, +0.13877787807814457E-15), (-0.11102230246251565E-15, +0.83266726846886741E-16), (+0.44408920985006262E-15, +0.26367796834847468E-15), (+0.0000000000000000, +0.19428902930940239E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.0000000000000000, -0.13877787807814457E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.0000000000000000, +0.38857805861880479E-15), (+0.22204460492503131E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (+0.33306690738754696E-15, +0.63837823915946501E-15), (+0.11102230246251565E-15, +0.55511151231257827E-15), (+0.11102230246251565E-15, +0.38857805861880479E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.91593399531575415E-15), (+0.22204460492503131E-15, +0.94368957093138306E-15)

334reltol = sqrt(epsilon(1._TKC))

335reltol

336+0.14901161193847656E-7

337isClose(data, atad(1:size(data)), reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+18

344data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

345data

346(+1.19215283084607781076082664727931738, +0.495934282686905322885551772123713299), (+1.60588291025287140924909112782944048, +0.435709444255745576163853264456998993), (+1.52423469423913176834045961713785196, +0.353860389821412420640920928217254775), (+1.91252719913873773594744448431632181, +0.611517335566374438091269968145943099), (+1.45191752505825143553826954303789178, +0.766025929212564868096536529027798843), (+1.57002092210485975238872338602654744, +0.823968954639482482754084778457766423), (+1.72861929005691570517973215858461214, +0.386032107935494054417835457661044263), (+1.09383667864698578537246224623527702, +0.462039506217859909337807221826649671), (+1.57962839516404172885866033213112045, +0.784257120081645136587942758358556428), (+1.71879215858218838473327185093194006, +0.960592718206947723902876817868396931E-1), (+1.60177005116610842821385522669072259, +0.800642773053774595264238482962703706), (+1.91823357513019305184946790642905214, +0.561156620152383149563308814375337532), (+1.44988461657752051837025698283347729, +0.795645275493552865198820988519015648E-1), (+1.45906182692562578549223309077068734, +0.343252234251102847986542948941951768), (+1.56144671487753404126304084194731573, +0.417688189489520064374741112297127086), (+1.14016378437917644977239986023657126, +0.907666936121816850130535167982457098), (+1.01557180541369918229831302498203862, +0.784005135885208576437307717487804857), (+1.07006099134447037176379917460005378, +0.381489921568084168093613094290482042)

347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.19215283084607781076082664727931738, +0.495934282686905322885551772123713299), (+1.60588291025287140924909112782944048, +0.435709444255745576163853264456998993), (+1.52423469423913176834045961713785234, +0.353860389821412420640920928217254534), (+1.91252719913873773594744448431632220, +0.611517335566374438091269968145943003), (+1.45191752505825143553826954303789197, +0.766025929212564868096536529027798650), (+1.57002092210485975238872338602654744, +0.823968954639482482754084778457766230), (+1.72861929005691570517973215858461234, +0.386032107935494054417835457661044166), (+1.09383667864698578537246224623527663, +0.462039506217859909337807221826649334), (+1.57962839516404172885866033213112026, +0.784257120081645136587942758358556428), (+1.71879215858218838473327185093193967, +0.960592718206947723902876817868396691E-1), (+1.60177005116610842821385522669072240, +0.800642773053774595264238482962703802), (+1.91823357513019305184946790642905214, +0.561156620152383149563308814375337725), (+1.44988461657752051837025698283347729, +0.795645275493552865198820988519015648E-1), (+1.45906182692562578549223309077068714, +0.343252234251102847986542948941951913), (+1.56144671487753404126304084194731573, +0.417688189489520064374741112297127471), (+1.14016378437917644977239986023657088, +0.907666936121816850130535167982457194), (+1.01557180541369918229831302498203862, +0.784005135885208576437307717487804953), (+1.07006099134447037176379917460005378, +0.381489921568084168093613094290482042), (+0.00000000000000000000000000000000000, +0.481482486096808963263994485646231830E-34), (-0.481482486096808963263994485646231830E-33, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, +0.240741243048404481631997242823115915E-33), (+0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (+0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (+0.288889491658085377958396691387739098E-33, +0.168518870133883137142398069976181140E-33), (+0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-33), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (+0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (+0.962964972193617926527988971292463659E-34, -0.505556610401649411427194209928543421E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34)

351reltol = sqrt(epsilon(1._TKC))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, atad(1:size(data)), reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+38

361data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

362data

363+1.42632520, +1.75592434, +1.64171958, +1.52880311, +1.33143234, +1.44573665, +1.88814020, +1.49262047, +1.35964179, +1.82214427, +1.67711973, +1.74836326, +1.23295569, +1.21342683, +1.41514611, +1.94935226, +1.60924470, +1.75860381, +1.13301182, +1.10459828, +1.97997117, +1.45882249, +1.80748487, +1.44470954, +1.99927175, +1.18909752, +1.96207190, +1.18591785, +1.02656257, +1.24156618, +1.85268569, +1.26978552, +1.18694186, +1.50287795, +1.97185886, +1.22087634, +1.71210623, +1.89598334

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.42632496, +1.75592422, +1.64171934, +1.52880299, +1.33143222, +1.44573665, +1.88814008, +1.49262023, +1.35964155, +1.82214403, +1.67711961, +1.74836302, +1.23295546, +1.21342707, +1.41514611, +1.94935226, +1.60924470, +1.75860381, +1.13301182, +1.10459828, +1.97997117, +1.45882261, +1.80748498, +1.44470978, +1.99927163, +1.18909752, +1.96207178, +1.18591797, +1.02656257, +1.24156618, +1.85268593, +1.26978540, +1.18694174, +1.50287795, +1.97185898, +1.22087634, +1.71210611, +1.89598322, +0.119209290E-6, +0.596046448E-7, +0.596046448E-7, -0.596046448E-7, +0.357627869E-6, +0.298023224E-6, +0.178813934E-6, -0.596046448E-7, +0.178813934E-6, +0.00000000, -0.119209290E-6, +0.00000000, +0.00000000, +0.00000000, +0.596046448E-7, -0.119209290E-6, -0.119209290E-6, -0.178813934E-6, +0.00000000, -0.119209290E-6, +0.119209290E-6, +0.00000000, +0.00000000, +0.596046448E-7, -0.596046448E-7, +0.00000000

368reltol = sqrt(epsilon(1._TKC))

369reltol

370+0.345266977E-3

371isClose(data, atad(1:size(data)), reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+49

378data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

379data

380+1.9680559576760106, +1.6081646983245470, +1.8897369280169973, +1.4204619585136069, +1.5668784775260263, +1.8429036937959444, +1.7174341697171280, +1.0733722152936347, +1.7551221549668172, +1.7347334815972668, +1.9431410096317818, +1.5976679977455253, +1.3271464066854883, +1.9586147402577487, +1.2190644885254187, +1.6854541556137805, +1.1383833629229159, +1.9169447442893122, +1.7450043829785891, +1.3045102685516969, +1.1241099539980719, +1.1623761423800798, +1.3215023368668120, +1.1612568686103477, +1.9607097902251511, +1.2191148843537378, +1.1179236211117027, +1.6743047266681830, +1.0795929288890114, +1.8909271301668369, +1.8464775731815934, +1.9096647326171068, +1.8470614345733725, +1.3521213568113724, +1.7985894151623723, +1.4095070174774440, +1.9513600845569712, +1.2334431805351547, +1.4633476081358929, +1.0532024543029701, +1.7370999587536597, +1.2297694999328543, +1.8926197498335546, +1.6849475479223899, +1.4658083543863167, +1.2767019548799254, +1.6824022945122283, +1.3229869447695108, +1.5280496897924247

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.9680559576760099, +1.6081646983245474, +1.8897369280169967, +1.4204619585136069, +1.5668784775260260, +1.8429036937959444, +1.7174341697171274, +1.0733722152936349, +1.7551221549668168, +1.7347334815972668, +1.9431410096317812, +1.5976679977455250, +1.3271464066854879, +1.9586147402577487, +1.2190644885254189, +1.6854541556137801, +1.1383833629229154, +1.9169447442893124, +1.7450043829785886, +1.3045102685516965, +1.1241099539980715, +1.1623761423800794, +1.3215023368668120, +1.1612568686103479, +1.9607097902251507, +1.2191148843537376, +1.1179236211117023, +1.6743047266681828, +1.0795929288890111, +1.8909271301668364, +1.8464775731815932, +1.9096647326171063, +1.8470614345733722, +1.3521213568113724, +1.7985894151623718, +1.4095070174774433, +1.9513600845569712, +1.2334431805351547, +1.4633476081358929, +1.0532024543029701, +1.7370999587536597, +1.2297694999328539, +1.8926197498335544, +1.6849475479223892, +1.4658083543863163, +1.2767019548799259, +1.6824022945122283, +1.3229869447695104, +1.5280496897924238, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.0000000000000000, +0.77715611723760958E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.77715611723760958E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.66613381477509392E-15, +0.12212453270876722E-14

385reltol = sqrt(epsilon(1._TKC))

386reltol

387+0.14901161193847656E-7

388isClose(data, atad(1:size(data)), reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+17

395data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

396data

397+1.53956792349605611705941450218418803, +1.56873973610800813885470789205223241, +1.59328839504505576425258620971057195, +1.97931170471297522529834219471847253, +1.04945575272705929950861531658480879, +1.24531823458438536557706920775639797, +1.61241242948238669232151519147801529, +1.62409348778579019817727941584310879, +1.71805351144505608740892727816811978, +1.28008092181360910918068634565576492, +1.10904950810271142781945794043206814, +1.59435558581059187073526600990259604, +1.56603191147757205565345125355212662, +1.35570521835952638438708857186459710, +1.42523016909429862455920510112788078, +1.07898218123637793370755604082632725, +1.76251531815631779452464498361836278

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.53956792349605611705941450218418803, +1.56873973610800813885470789205223222, +1.59328839504505576425258620971057234, +1.97931170471297522529834219471847291, +1.04945575272705929950861531658480879, +1.24531823458438536557706920775639797, +1.61241242948238669232151519147801529, +1.62409348778579019817727941584310899, +1.71805351144505608740892727816811997, +1.28008092181360910918068634565576492, +1.10904950810271142781945794043206814, +1.59435558581059187073526600990259623, +1.56603191147757205565345125355212700, +1.35570521835952638438708857186459730, +1.42523016909429862455920510112788117, +1.07898218123637793370755604082632706, +1.76251531815631779452464498361836278, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000

402reltol = sqrt(epsilon(1._TKC))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, atad(1:size(data)), reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+61

412data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

413data

414(+1.40605998, +0.565157294), (+1.93959773, +0.659429431), (+1.97772634, +0.701774955), (+1.21612167, +0.286120236), (+1.82844567, +0.751487911), (+1.46730828, +0.668015361), (+1.29655576, +0.735564590), (+1.61647618, +0.475679040), (+1.87749243, +0.497945487), (+1.60355663, +0.693369031), (+1.33326864, +0.745647550E-1), (+1.09635615, +0.345367610), (+1.00107694, +0.140347540), (+1.12696397, +0.300351143), (+1.80858946, +0.578002155), (+1.05032682, +0.601898670), (+1.56578791, +0.889310181), (+1.95225573, +0.117885113), (+1.62949944, +0.279742301), (+1.79904604, +0.147764444), (+1.51313758, +0.515594661), (+1.50797105, +0.326288164), (+1.28768396, +0.855134606), (+1.06342793, +0.201727211), (+1.39880228, +0.363100827), (+1.69217789, +0.312558413), (+1.98800373, +0.751050591), (+1.90752101, +0.600333750), (+1.67071390, +0.397202075), (+1.26246786, +0.921101630), (+1.35895145, +0.500023365E-3), (+1.06067920, +0.582194626), (+1.52207065, +0.714689612), (+1.36858916, +0.603426099E-1), (+1.72377157, +0.196810603), (+1.87006879, +0.510949910), (+1.22937059, +0.564819574), (+1.48236275, +0.912687123), (+1.80832219, +0.443449318), (+1.38919067, +0.927007854), (+1.57748222, +0.870593369), (+1.41332722, +0.666785598), (+1.54116333, +0.930433989), (+1.89263511, +0.339801371), (+1.16486740, +0.394899964), (+1.65057111, +0.835630238), (+1.14963937, +0.529663026), (+1.65035069, +0.278297007), (+1.22308111, +0.417182148), (+1.85399318, +0.445932746), (+1.46752548, +0.230862916), (+1.69758809, +0.852900743E-2), (+1.82428932, +0.971226335), (+1.45349371, +0.890302062E-1), (+1.15924811, +0.324518800), (+1.98197865, +0.260514021E-2), (+1.02324986, +0.609044194), (+1.11961102, +0.417855680), (+1.01079571, +0.586911738), (+1.57788563, +0.463087142), (+1.42749715, +0.545256257)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.40606010, +0.565157235), (+1.93959785, +0.659429431), (+1.97772646, +0.701774895), (+1.21612167, +0.286120296), (+1.82844579, +0.751487970), (+1.46730828, +0.668015420), (+1.29655588, +0.735564590), (+1.61647618, +0.475678921), (+1.87749255, +0.497945547), (+1.60355675, +0.693369031), (+1.33326888, +0.745649338E-1), (+1.09635627, +0.345367610), (+1.00107729, +0.140347451), (+1.12696409, +0.300351292), (+1.80858934, +0.578002334), (+1.05032670, +0.601898909), (+1.56578803, +0.889310122), (+1.95225573, +0.117885172), (+1.62949955, +0.279742271), (+1.79904580, +0.147764504), (+1.51313770, +0.515594602), (+1.50797117, +0.326288134), (+1.28768420, +0.855134487), (+1.06342781, +0.201727197), (+1.39880252, +0.363100857), (+1.69217801, +0.312558413), (+1.98800373, +0.751050711), (+1.90752101, +0.600333691), (+1.67071414, +0.397202134), (+1.26246786, +0.921101570), (+1.35895133, +0.500202179E-3), (+1.06067920, +0.582194567), (+1.52207077, +0.714689553), (+1.36858940, +0.603426397E-1), (+1.72377181, +0.196810544), (+1.87006879, +0.510949850), (+1.22937071, +0.564819574), (+1.48236275, +0.912687123), (+1.80832231, +0.443449289), (+1.38919055, +0.927007794), (+1.57748234, +0.870593309), (+1.41332734, +0.666785479), (+1.54116368, +0.930433750), (+1.89263499, +0.339801431), (+1.16486752, +0.394899935), (+1.65057087, +0.835630298), (+1.14963925, +0.529663205), (+1.65035045, +0.278297096), (+1.22308111, +0.417182088), (+1.85399318, +0.445932746), (+1.46752560, +0.230862945), (+1.69758797, +0.852909684E-2), (+1.82428944, +0.971226335), (+1.45349395, +0.890303552E-1), (+1.15924835, +0.324518800), (+1.98197854, +0.260515511E-2), (+1.02325010, +0.609044194), (+1.11961126, +0.417855620), (+1.01079607, +0.586911678), (+1.57788587, +0.463087082), (+1.42749739, +0.545256197), (+0.417232513E-6, -0.208616257E-6), (+0.238418579E-6, +0.596046448E-7), (+0.298023224E-6, +0.149011612E-6)

419reltol = sqrt(epsilon(1._TKC))

420reltol

421+0.345266977E-3

422isClose(data, atad(1:size(data)), reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+70

429data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

430data

431(+1.9238399766022813, +0.85239173410685842), (+1.7194117923863712, +0.21651625309711220), (+1.2293927682414969, +0.87218397136378556), (+1.4001771832044363, +0.65169780217611617), (+1.7496806500295219, +0.30195315111351873E-1), (+1.7844936596082168, +0.23972063744828886), (+1.6251836331321636, +0.74025330940458234), (+1.1939277083488342, +0.43027725716158371), (+1.8000447913031490, +0.47776035218363122), (+1.3177873338346449, +0.18549050641960296), (+1.6949423357574327, +0.86510010160977624), (+1.7444120041152207, +0.81795387294870070), (+1.0163782512433275, +0.26473858616902546E-1), (+1.9422306267146867, +0.64871798118259028), (+1.2537745203754067, +0.29280084230615722), (+1.3752211419132654, +0.85947943911725122), (+1.4640517532596324, +0.72352994378674318), (+1.5306586774021902, +0.33395329101209348E-1), (+1.8275037295269709, +0.73434131560489968), (+1.9531417318686159, +0.94759177529802818), (+1.7123041802894718, +0.95646442020117761), (+1.2828245718550355, +0.51873412619657655), (+1.3743667099866501, +0.95196997284101847), (+1.6841587397979905, +0.22430888020472695), (+1.3841972270659837, +0.81448525538912753), (+1.7835073046740746, +0.35021706718850298E-1), (+1.6626493056649663, +0.43623943495205630), (+1.8218821487232002, +0.48741061380271511), (+1.8054416712009864, +0.50692479283126091), (+1.4943475627851091, +0.28154907452800693E-1), (+1.3140019692887517, +0.47945698977309292), (+1.0845243770437616, +0.97604826571785985), (+1.9128627569086334, +0.47244454658793700), (+1.0892379857959873, +0.31032696443362873), (+1.1141388839829163, +0.89854870633563921), (+1.7180877273560113, +0.66875018823336430), (+1.0052046354883508, +0.47657039705814419), (+1.1000540292596739, +0.51568806970497472), (+1.3055191872283216, +0.79552347381270883), (+1.5624649204063785, +0.57734525002020576), (+1.7914748128645446, +0.33581656183096398), (+1.0122476743825817, +0.12296939377960026), (+1.1565720719769002, +0.47673914821597407), (+1.5159952257493321, +0.33086735342578999), (+1.0687998099562726, +0.75975817666751344), (+1.3451831066996904, +0.36924105821312114E-1), (+1.6425026356718382, +0.26552117449472656), (+1.7877993911757479, +0.27977701984355574), (+1.5950905283265202, +0.89362913536263733), (+1.9158129697039596, +0.53199764309327291), (+1.1052282237265725, +0.70011302996478419), (+1.2016455150333316, +0.48604943945006907), (+1.7070626078530262, +0.75452208161055967), (+1.9410885932944755, +0.22613477653855696), (+1.8441180772317693, +0.64664446976982071), (+1.9653355829765666, +0.32052225582071914), (+1.1980155884766188, +0.54454376746392164), (+1.1808963396134220, +0.11749221292895162), (+1.2094169262183663, +0.73764123969449580), (+1.5831248101886040, +0.99435607002668203), (+1.7378630260827534, +0.61963758321703111), (+1.6331578727802898, +0.40453522465686564E-2), (+1.5165711293391002, +0.83086967447497251), (+1.6822042183546579, +0.40732734758563283), (+1.1470526173036268, +0.15427634748446151), (+1.1088558352595674, +0.33202337538524196), (+1.5463344249871249, +0.95674338753927513), (+1.1143286113060094, +0.31465687451673019), (+1.8734841145635455, +0.34032877363726932), (+1.9138207411999499, +0.62860936368762699)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.9238399766022811, +0.85239173410685831), (+1.7194117923863714, +0.21651625309711223), (+1.2293927682414969, +0.87218397136378600), (+1.4001771832044363, +0.65169780217611639), (+1.7496806500295212, +0.30195315111351956E-1), (+1.7844936596082168, +0.23972063744828928), (+1.6251836331321634, +0.74025330940458267), (+1.1939277083488340, +0.43027725716158371), (+1.8000447913031490, +0.47776035218363128), (+1.3177873338346453, +0.18549050641960302), (+1.6949423357574323, +0.86510010160977657), (+1.7444120041152207, +0.81795387294870125), (+1.0163782512433275, +0.26473858616902435E-1), (+1.9422306267146865, +0.64871798118259050), (+1.2537745203754065, +0.29280084230615744), (+1.3752211419132649, +0.85947943911725133), (+1.4640517532596320, +0.72352994378674318), (+1.5306586774021902, +0.33395329101209334E-1), (+1.8275037295269705, +0.73434131560489968), (+1.9531417318686157, +0.94759177529802818), (+1.7123041802894714, +0.95646442020117739), (+1.2828245718550355, +0.51873412619657644), (+1.3743667099866497, +0.95196997284101814), (+1.6841587397979902, +0.22430888020472681), (+1.3841972270659832, +0.81448525538912731), (+1.7835073046740746, +0.35021706718850382E-1), (+1.6626493056649658, +0.43623943495205614), (+1.8218821487232000, +0.48741061380271522), (+1.8054416712009860, +0.50692479283126080), (+1.4943475627851086, +0.28154907452800693E-1), (+1.3140019692887512, +0.47945698977309265), (+1.0845243770437611, +0.97604826571785952), (+1.9128627569086329, +0.47244454658793666), (+1.0892379857959873, +0.31032696443362850), (+1.1141388839829163, +0.89854870633563921), (+1.7180877273560116, +0.66875018823336430), (+1.0052046354883508, +0.47657039705814375), (+1.1000540292596743, +0.51568806970497449), (+1.3055191872283216, +0.79552347381270860), (+1.5624649204063785, +0.57734525002020587), (+1.7914748128645441, +0.33581656183096398), (+1.0122476743825817, +0.12296939377960016), (+1.1565720719768997, +0.47673914821597396), (+1.5159952257493321, +0.33086735342579010), (+1.0687998099562726, +0.75975817666751333), (+1.3451831066996900, +0.36924105821312198E-1), (+1.6425026356718377, +0.26552117449472640), (+1.7877993911757479, +0.27977701984355546), (+1.5950905283265198, +0.89362913536263688), (+1.9158129697039596, +0.53199764309327280), (+1.1052282237265723, +0.70011302996478375), (+1.2016455150333312, +0.48604943945006884), (+1.7070626078530258, +0.75452208161055911), (+1.9410885932944753, +0.22613477653855646), (+1.8441180772317691, +0.64664446976981971), (+1.9653355829765662, +0.32052225582071892), (+1.1980155884766184, +0.54454376746392152), (+1.1808963396134220, +0.11749221292895143), (+1.2094169262183661, +0.73764123969449480), (+1.5831248101886037, +0.99435607002668158), (+1.7378630260827532, +0.61963758321703055), (+1.6331578727802896, +0.40453522465681308E-2), (+1.5165711293391002, +0.83086967447497162), (+1.6822042183546575, +0.40732734758563227), (+1.1470526173036266, +0.15427634748446134), (+1.1088558352595672, +0.33202337538524218), (+1.5463344249871249, +0.95674338753927479), (+1.1143286113060094, +0.31465687451673013), (+1.8734841145635450, +0.34032877363726888), (+1.9138207411999497, +0.62860936368762677), (+0.0000000000000000, -0.27755575615628914E-15), (-0.22204460492503131E-15, -0.44408920985006262E-15), (-0.33306690738754696E-15, -0.16653345369377348E-15), (-0.11102230246251565E-15, -0.23592239273284576E-15), (+0.11102230246251565E-15, -0.44408920985006262E-15), (+0.0000000000000000, -0.49960036108132044E-15), (+0.11102230246251565E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, -0.49960036108132044E-15), (+0.22204460492503131E-15, -0.30531133177191805E-15), (+0.33306690738754696E-15, -0.27755575615628914E-15), (-0.11102230246251565E-15, -0.33306690738754696E-15), (-0.11102230246251565E-15, -0.12490009027033011E-15), (+0.22204460492503131E-15, -0.16653345369377348E-15), (+0.22204460492503131E-15, -0.11102230246251565E-15), (+0.11102230246251565E-15, +0.0000000000000000), (+0.44408920985006262E-15, -0.33306690738754696E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.44408920985006262E-15, -0.13877787807814457E-15), (+0.22204460492503131E-15, +0.0000000000000000), (+0.11102230246251565E-15, -0.27755575615628914E-16), (+0.11102230246251565E-15, -0.55511151231257827E-16), (+0.33306690738754696E-15, -0.38857805861880479E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.33306690738754696E-15, -0.85001450322863548E-16), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.55511151231257827E-15, +0.55511151231257827E-16), (-0.22204460492503131E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, -0.27755575615628914E-16), (-0.33306690738754696E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, -0.22204460492503131E-15), (-0.11102230246251565E-15, +0.24980018054066022E-15), (+0.0000000000000000, +0.11102230246251565E-15), (-0.11102230246251565E-15, +0.38857805861880479E-15), (+0.11102230246251565E-15, -0.55511151231257827E-16), (+0.11102230246251565E-15, -0.11102230246251565E-15), (+0.0000000000000000, -0.15265566588595902E-15), (+0.11102230246251565E-15, +0.83266726846886741E-16), (+0.22204460492503131E-15, -0.22204460492503131E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.33306690738754696E-15, +0.83266726846886741E-16), (+0.0000000000000000, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.16653345369377348E-15), (-0.22204460492503131E-15, +0.22204460492503131E-15), (+0.0000000000000000, +0.11102230246251565E-15), (-0.11102230246251565E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.62450045135165055E-15), (+0.0000000000000000, +0.11102230246251565E-14), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.83266726846886741E-16), (-0.33306690738754696E-15, +0.66613381477509392E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (-0.22204460492503131E-15, +0.55511151231257827E-15), (+0.44408920985006262E-15, +0.72337968948232856E-15), (-0.33306690738754696E-15, +0.77715611723760958E-15), (+0.55511151231257827E-15, +0.69388939039072284E-15)

436reltol = sqrt(epsilon(1._TKC))

437reltol

438+0.14901161193847656E-7

439isClose(data, atad(1:size(data)), reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+47

446data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

447data

448(+1.87381941861238216359586733633605106, +0.238324632301248969452962971282649390), (+1.57722609149935372328390830442186373, +0.133667493319442143795519354965516054), (+1.10895130389975787316567593598817112, +0.424810938426054002741633167739818192), (+1.25177800042004289414656036528806988, +0.273571155897833470154497993945863731), (+1.28240114422925790581427133972122548, +0.342040255670353366815316052180160423), (+1.88146343976985301416388044566869220, +0.317485490300175104270807975218903752), (+1.18736707162468008713431079620093067, +0.569192991335865292610575614224638477), (+1.82575923883551355860007624878124346, +0.146171650587460154257727514965825437), (+1.70750224221753907130719958544068858, +0.442166043573182066914185792945588961), (+1.36403338256120012485654640666306485, +0.667838537361383223363825743764100411), (+1.12848462504094223979336796987406907, +0.944525209775727569406767068519670682), (+1.97424240891448133753965491478371149, +0.609695832199103235220656449393909418), (+1.30599385960258677553307104430548479, +0.263486173986985702083441247394522237), (+1.19867811816776964317107048713771051, +0.605143300037684709710301536881871969), (+1.50547052818738579884967413200338023, +0.782241182360282754596609115130207033), (+1.87164544099350506661846831860582795, +0.418642396618771366571600968534530759), (+1.56398662547622730455742015506517554, +0.653276481601325306289367330915617601), (+1.52635777081495167549489923161535285, +0.987577700588214302162577698051752373), (+1.42740996163084024430136637189376257, +0.962242454929406871074633037517492261), (+1.73663676672424669220519362842884843, +0.358968615073073398990609956518038018), (+1.01990441951430067459025825630956460, +0.696591769724791123619519990175898521), (+1.09836617414943966432213647524336119, +0.395042588350001739026647265322431865), (+1.29978413676899891434787669525854117, +0.773246326133521768322323013121200082), (+1.98011560567980895910874246906046229, +0.235311089789169253249580493758115336), (+1.33407189291693258129249568029862511, +0.973400471544986280130487921755215712), (+1.36596017834328992848817808209911620, +0.941740265836123387267029268399603703), (+1.64223042276921742161778851111722974, +0.774356565813171754354489668297974908), (+1.29473506837011152404075908467520130, +0.570749674968522227638551856832423778), (+1.02270619752124118943773639444523453, +0.923699087496274756956648429892409994), (+1.20665205245244916673104422344495429, +0.434888040954917977358120219004115750), (+1.85500053147309864859369135082156016, +0.525457347004871585955412785888156047), (+1.36580061020352788265669665022858904, +0.554897959902871384576337848030849175), (+1.18580859062185761007331241284406863, +0.629890872534355272540803171027244519), (+1.29679194072800498624579851394892857, +0.436416907198981850436740344507552564), (+1.27459782135126063086953367155734497, +0.323099843335360623625045209768981568), (+1.04055513522292034220492640322160044, +0.220519548117454291036659695658245587), (+1.55889936003762602759233356589601531, +0.325442397766961110448406836064857912), (+1.15789327367804587660838966179943576, +0.413878965494873086277868772831592529), (+1.55947068766122340675977100954759213, +0.357179540035316493523368397579988829), (+1.07618068096219356595355826374355404, +0.748536139976091703759887435842090698), (+1.33488771863720427786977531242089047, +0.815629202789498421240102534969647617), (+1.54939844078279263178376103890291800, +0.981035132772531464345765229710582713), (+1.47235020956270904032785631991706358, +0.729041255631077166645831812195252950), (+1.76839883739969377813377099422382256, +0.525090553744489804883307346111273428E-1), (+1.76756516575713749387364541374956026, +0.294050067981681568530782256011099303), (+1.78398290837780403265006174854978853, +0.941750771919413863678090433375208633), (+1.52247270220179897773376284969688073, +0.952402414177342509422198597098454681)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.87381941861238216359586733633605125, +0.238324632301248969452962971282649390), (+1.57722609149935372328390830442186373, +0.133667493319442143795519354965516006), (+1.10895130389975787316567593598817131, +0.424810938426054002741633167739818240), (+1.25177800042004289414656036528806969, +0.273571155897833470154497993945863635), (+1.28240114422925790581427133972122548, +0.342040255670353366815316052180160182), (+1.88146343976985301416388044566869220, +0.317485490300175104270807975218903608), (+1.18736707162468008713431079620093105, +0.569192991335865292610575614224638188), (+1.82575923883551355860007624878124327, +0.146171650587460154257727514965825051), (+1.70750224221753907130719958544068839, +0.442166043573182066914185792945589009), (+1.36403338256120012485654640666306485, +0.667838537361383223363825743764100508), (+1.12848462504094223979336796987406946, +0.944525209775727569406767068519670778), (+1.97424240891448133753965491478371091, +0.609695832199103235220656449393909515), (+1.30599385960258677553307104430548479, +0.263486173986985702083441247394522430), (+1.19867811816776964317107048713771071, +0.605143300037684709710301536881872162), (+1.50547052818738579884967413200338042, +0.782241182360282754596609115130207226), (+1.87164544099350506661846831860582737, +0.418642396618771366571600968534530951), (+1.56398662547622730455742015506517573, +0.653276481601325306289367330915617601), (+1.52635777081495167549489923161535247, +0.987577700588214302162577698051752373), (+1.42740996163084024430136637189376257, +0.962242454929406871074633037517491972), (+1.73663676672424669220519362842884804, +0.358968615073073398990609956518037922), (+1.01990441951430067459025825630956460, +0.696591769724791123619519990175898617), (+1.09836617414943966432213647524336080, +0.395042588350001739026647265322431673), (+1.29978413676899891434787669525854136, +0.773246326133521768322323013121199889), (+1.98011560567980895910874246906046229, +0.235311089789169253249580493758115240), (+1.33407189291693258129249568029862511, +0.973400471544986280130487921755215615), (+1.36596017834328992848817808209911582, +0.941740265836123387267029268399603607), (+1.64223042276921742161778851111722974, +0.774356565813171754354489668297974523), (+1.29473506837011152404075908467520091, +0.570749674968522227638551856832423489), (+1.02270619752124118943773639444523434, +0.923699087496274756956648429892409897), (+1.20665205245244916673104422344495390, +0.434888040954917977358120219004115798), (+1.85500053147309864859369135082156016, +0.525457347004871585955412785888155855), (+1.36580061020352788265669665022858885, +0.554897959902871384576337848030848886), (+1.18580859062185761007331241284406882, +0.629890872534355272540803171027244711), (+1.29679194072800498624579851394892838, +0.436416907198981850436740344507552324), (+1.27459782135126063086953367155734516, +0.323099843335360623625045209768981231), (+1.04055513522292034220492640322160025, +0.220519548117454291036659695658245298), (+1.55889936003762602759233356589601531, +0.325442397766961110448406836064857864), (+1.15789327367804587660838966179943557, +0.413878965494873086277868772831592384), (+1.55947068766122340675977100954759271, +0.357179540035316493523368397579988732), (+1.07618068096219356595355826374355384, +0.748536139976091703759887435842090987), (+1.33488771863720427786977531242089028, +0.815629202789498421240102534969647520), (+1.54939844078279263178376103890291819, +0.981035132772531464345765229710582809), (+1.47235020956270904032785631991706396, +0.729041255631077166645831812195252661), (+1.76839883739969377813377099422382237, +0.525090553744489804883307346111271984E-1), (+1.76756516575713749387364541374956026, +0.294050067981681568530782256011099496), (+1.78398290837780403265006174854978834, +0.941750771919413863678090433375208730), (+1.52247270220179897773376284969688092, +0.952402414177342509422198597098454777), (-0.481482486096808963263994485646231830E-33, +0.722223729145213444895991728469347744E-34), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (+0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, +0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.674075480535532548569592279904724561E-33, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.385185988877447170611195588516985464E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (+0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (+0.481482486096808963263994485646231830E-33, +0.240741243048404481631997242823115915E-33), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, -0.337037740267766274284796139952362281E-33), (-0.962964972193617926527988971292463659E-34, -0.433334237487128066937595037081608647E-33), (+0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34), (-0.577778983316170755916793382775478196E-33, +0.144444745829042688979198345693869549E-33)

453reltol = sqrt(epsilon(1._TKC))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, atad(1:size(data)), reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+98

463data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

464data

465+1.46773815, +1.47035265, +1.39888310, +1.00660133, +1.19729328, +1.82445884, +1.17608881, +1.83541334, +1.63246679, +1.72602010, +1.14014804, +1.25314343, +1.26571345, +1.66560411, +1.51457310, +1.65378547, +1.80419350, +1.38188601, +1.50347745, +1.33203793, +1.10655522, +1.72957730, +1.54572010, +1.95910144, +1.34340262, +1.04477835, +1.98445487, +1.49759197, +1.18971586, +1.07133162, +1.02727818, +1.12285089, +1.69307566, +1.33101809, +1.00175238, +1.02703154, +1.16491365, +1.92122495, +1.39998448, +1.76231349, +1.42362714, +1.47499740, +1.75639987, +1.60060954, +1.64632714, +1.74200642, +1.28446078, +1.10423577, +1.65392947, +1.05116725, +1.01585114, +1.23786831, +1.68927121, +1.10259295, +1.68467498, +1.27888036, +1.72014785, +1.61277676, +1.70034528, +1.20155621, +1.62957215, +1.96223164, +1.32171309, +1.11959934, +1.68797302, +1.10710645, +1.29307294, +1.75232720, +1.33034480, +1.09349823, +1.44618130, +1.07163048, +1.12537050, +1.51201427, +1.60719526, +1.48364484, +1.06990802, +1.53054810, +1.74378920, +1.83575177, +1.95381701, +1.28631091, +1.24362111, +1.54289854, +1.87980485, +1.34407377, +1.51758146, +1.62687218, +1.64440870, +1.13271761, +1.59843898, +1.27685976, +1.82806683, +1.71767747, +1.78049779, +1.10552061, +1.22963011, +1.97397077

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.46773815, +1.47035301, +1.39888299, +1.00660157, +1.19729292, +1.82445884, +1.17608857, +1.83541322, +1.63246679, +1.72602022, +1.14014804, +1.25314367, +1.26571333, +1.66560388, +1.51457286, +1.65378547, +1.80419338, +1.38188624, +1.50347710, +1.33203828, +1.10655534, +1.72957742, +1.54572022, +1.95910144, +1.34340262, +1.04477847, +1.98445463, +1.49759233, +1.18971610, +1.07133186, +1.02727795, +1.12285101, +1.69307554, +1.33101821, +1.00175214, +1.02703154, +1.16491365, +1.92122507, +1.39998424, +1.76231325, +1.42362702, +1.47499752, +1.75639963, +1.60060978, +1.64632726, +1.74200654, +1.28446054, +1.10423565, +1.65392923, +1.05116737, +1.01585102, +1.23786819, +1.68927121, +1.10259318, +1.68467474, +1.27888012, +1.72014761, +1.61277676, +1.70034516, +1.20155632, +1.62957227, +1.96223187, +1.32171309, +1.11959934, +1.68797302, +1.10710680, +1.29307306, +1.75232720, +1.33034480, +1.09349847, +1.44618106, +1.07163048, +1.12537050, +1.51201451, +1.60719526, +1.48364508, +1.06990778, +1.53054833, +1.74378896, +1.83575177, +1.95381677, +1.28631115, +1.24362087, +1.54289877, +1.87980473, +1.34407389, +1.51758134, +1.62687206, +1.64440846, +1.13271773, +1.59843874, +1.27685988, +1.82806659, +1.71767771, +1.78049755, +1.10552084, +1.22963011, +1.97397113, +0.596046448E-7, +0.238418579E-6, +0.178813934E-6, +0.476837158E-6, +0.119209290E-6, +0.357627869E-6, +0.00000000, +0.596046448E-7, -0.238418579E-6, +0.119209290E-6, -0.178813934E-6, +0.298023224E-6, -0.596046448E-7, +0.178813934E-6, +0.238418579E-6, +0.357627869E-6, +0.238418579E-6, +0.238418579E-6, +0.178813934E-6, +0.417232513E-6, +0.119209290E-6, +0.178813934E-6, +0.476837158E-6, +0.238418579E-6, +0.357627869E-6, +0.119209290E-6, +0.119209290E-6, +0.178813934E-6, -0.119209290E-6, +0.00000000

470reltol = sqrt(epsilon(1._TKC))

471reltol

472+0.345266977E-3

473isClose(data, atad(1:size(data)), reltol = reltol)

474T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+60

480data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

481data

482+1.3459920804016170, +1.7441306750319105, +1.2133513259150439, +1.4149128591433677, +1.8929000371124256, +1.4900841576889154, +1.4141788167709914, +1.3028492133312768, +1.3667757292926281, +1.6464879885496790, +1.8176260670712949, +1.7376873180382364, +1.8357597351811186, +1.6342404331449489, +1.1947197916885823, +1.5306593195974454, +1.5237062653592455, +1.1505750475484118, +1.8945072455149998, +1.2053487616082017, +1.0551904238460632, +1.1394508628358819, +1.1920162490412149, +1.5067766423351183, +1.4625178892956299, +1.3371225155674618, +1.9506899562044246, +1.5839867081394341, +1.3354670475226555, +1.9744271070046375, +1.7057465030900929, +1.4131049872277468, +1.4184799072385308, +1.7306952847592671, +1.9567977215130345, +1.5956156774319612, +1.1209828566117181, +1.9745337768147508, +1.4595810272584191, +1.2983178505908182, +1.7036016401236078, +1.4977430843326378, +1.1879663121695905, +1.0434038689805507, +1.3398313547588869, +1.3781441311686049, +1.2963034902259936, +1.8396491239207082, +1.6777748982969893, +1.3862060519029962, +1.8533448779423352, +1.1167187292138383, +1.1584968008209056, +1.5408001081530616, +1.1943046096463319, +1.1625486155103739, +1.9285988379718342, +1.1866235263172014, +1.4505288263809786, +1.9330547289849287

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.3459920804016170, +1.7441306750319114, +1.2133513259150437, +1.4149128591433682, +1.8929000371124249, +1.4900841576889157, +1.4141788167709910, +1.3028492133312772, +1.3667757292926279, +1.6464879885496790, +1.8176260670712945, +1.7376873180382368, +1.8357597351811181, +1.6342404331449494, +1.1947197916885823, +1.5306593195974452, +1.5237062653592455, +1.1505750475484120, +1.8945072455149994, +1.2053487616082019, +1.0551904238460625, +1.1394508628358822, +1.1920162490412149, +1.5067766423351183, +1.4625178892956299, +1.3371225155674620, +1.9506899562044242, +1.5839867081394343, +1.3354670475226551, +1.9744271070046373, +1.7057465030900927, +1.4131049872277468, +1.4184799072385308, +1.7306952847592676, +1.9567977215130341, +1.5956156774319612, +1.1209828566117179, +1.9745337768147508, +1.4595810272584191, +1.2983178505908182, +1.7036016401236076, +1.4977430843326380, +1.1879663121695905, +1.0434038689805512, +1.3398313547588865, +1.3781441311686051, +1.2963034902259936, +1.8396491239207082, +1.6777748982969891, +1.3862060519029964, +1.8533448779423347, +1.1167187292138381, +1.1584968008209049, +1.5408001081530618, +1.1943046096463319, +1.1625486155103739, +1.9285988379718340, +1.1866235263172014, +1.4505288263809786, +1.9330547289849289, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.77715611723760958E-15, +0.55511151231257827E-15

487reltol = sqrt(epsilon(1._TKC))

488reltol

489+0.14901161193847656E-7

490isClose(data, atad(1:size(data)), reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+70

497data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

498data

499+1.87355834975058325837364689756940937, +1.75002265136413691550941969563499911, +1.00166587436618001177186513819009902, +1.25384611028440749768665606565974399, +1.15803712912436629324606034577865492, +1.81065196754123809174130524252945711, +1.47981443117224821238963853036737818, +1.20576899032387856860473704008661290, +1.45205195742790161769895671606622116, +1.89002926693236185219126843755630629, +1.77719333520033152297524347486490795, +1.27928673273103312047570949039058910, +1.07724959631415677024342433391123647, +1.57488974852754415929381270496140376, +1.63645582543162789173564091925785333, +1.54213523237040294851888949263824000, +1.31412539953280858282996506912836979, +1.44400281063234207811407038373549830, +1.63700398488596556713029297072183395, +1.46498225552020719641482095322036161, +1.12109130624031302212368881718819310, +1.59659732077328208684357659578165141, +1.06122249833862484404753737994426276, +1.19109884156434131455364720253237632, +1.19292429956549991744306709811740944, +1.05409532496517627555760982751401209, +1.18472644288780118153020620700129125, +1.33562213412807603304155218846046379, +1.85958465704776606294285676629648439, +1.24966567199395401989424651298419140, +1.79720885261891900931415649601687541, +1.50547874836006003254214095362864314, +1.30534359043457742501767967669384222, +1.59705962895472444938318724758507539, +1.48394987267543520873670246824479047, +1.02789821045625134345625582238906463, +1.25176716685291343190185819915068070, +1.35292027962157954039237450531168269, +1.72741980158772998802904095050774046, +1.69126530359569575220041965384993324, +1.59808065260541832472054343343981184, +1.98180695922976519279285755702424486, +1.37822819127555617448252126614104777, +1.22763882226185532101639876812747400, +1.29443529839643089791178599164589120, +1.89111282397556698190485494370351459, +1.87293980170533909364241116478843908, +1.02708100345968614438381588553465677, +1.36833013109474623698699026019919074, +1.21140473641524383607340619251075966, +1.94229992384906331415003046708626733, +1.37299248410757314623062442221480482, +1.53343028046045322581648687619823089, +1.28746579445053847998053771589186633, +1.09774978803743296646748911507079005, +1.30139529463576380694805720366173961, +1.65973951166409148210792196564304113, +1.45293483865794768113984805069961527, +1.62745864057103388664559764332567271, +1.51669628903149705250183148842347740, +1.25355662520091972583123209618522339, +1.83507955729617063653012722017898048, +1.48471559196525028268481234361045410, +1.70259150710089127258308938063424590, +1.00875906167260785134072302625123781, +1.41949368888485540408666407212853106, +1.56379221557323229511605610736767431, +1.55675207500506650253244165516278170, +1.17115927540884865657226868277676878, +1.81189964742350271846813802397333088

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.87355834975058325837364689756940937, +1.75002265136413691550941969563499930, +1.00166587436618001177186513819009902, +1.25384611028440749768665606565974399, +1.15803712912436629324606034577865472, +1.81065196754123809174130524252945711, +1.47981443117224821238963853036737799, +1.20576899032387856860473704008661290, +1.45205195742790161769895671606622174, +1.89002926693236185219126843755630668, +1.77719333520033152297524347486490853, +1.27928673273103312047570949039058910, +1.07724959631415677024342433391123685, +1.57488974852754415929381270496140356, +1.63645582543162789173564091925785372, +1.54213523237040294851888949263823962, +1.31412539953280858282996506912836979, +1.44400281063234207811407038373549811, +1.63700398488596556713029297072183395, +1.46498225552020719641482095322036161, +1.12109130624031302212368881718819310, +1.59659732077328208684357659578165141, +1.06122249833862484404753737994426276, +1.19109884156434131455364720253237632, 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-0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33, -0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33, +0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, -0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, +0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-33, -0.385185988877447170611195588516985464E-33, +0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33

504reltol = sqrt(epsilon(1._TKC))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, atad(1:size(data)), reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

510

511

Test:: test_pm_fftnr

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, you must acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library, you must also ask the end users to cite this original ParaMonte library.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 428 of file pm_fftnr.F90.

The documentation for this interface was generated from the following file:

/home/amir/git/paramonte/src/fortran/main/pm_fftnr.F90